Apparatus and method for superposition transmissions

ABSTRACT

Apparatuses, systems, and methods are described concerning a new type of superposition multiplexing transmission constellation (super-constellation): the Gray-mapped Non-uniform-capable Constellation (GNC). Apparatuses, systems, and methods for generating GNC super-constellations are described, as well as apparatuses, systems, and methods for receiving, demapping, and decoding transmissions using GNC super-constellations. Apparatuses, systems, and methods for selecting a type of superposition multiplexing transmission constellation based on various conditions are also described.

PRIORITY

This application is a Divisional Application of U.S. patent applicationSer. No. 14/997,106, which was filed in the United States Patent andTrademark Office (USPTO) on Jan. 15, 2016, and claims priority under 35U.S.C. § 119(e) to U.S. Provisional Patent Application Ser. No.62/173,241, which was filed in the USPTO on Jun. 9, 2015, U.S.Provisional Patent Application Ser. No. 62/203,818, which was filed inthe USPTO on Aug. 11, 2015, U.S. Provisional Patent Application Ser. No.62/204,305, which was filed in the USPTO on Aug. 12, 2015, and U.S.Provisional Patent Application Ser. No. 62/210,326, which was filed inthe USPTO on Aug. 26, 2015, the entire content of each of which isincorporated herein by reference.

FIELD OF THE DISCLOSURE

The present disclosure relates generally to superposition multipleaccess communication technologies, and more particularly, to Multi-UserSuperposition Transmission (MUST) in 3^(rd) Generation PartnershipProject (3GPP).

BACKGROUND

The adoption of superposition multiple access is a recent development inthe 3^(rd) Generation Partnership Project (3GPP). See, e.g., Chairman'sNotes, 3GPP RAN1 Meeting #80b, Belgrade (Apr. 20, 2014). Although oftenreferred to in 3GPP as Multi-User Superposition Transmission (MUST),superposition multiple access techniques has various names and varioustypes, including, and not limited to, Non-Orthogonal Multiple Access(NOMA), Semi-Orthogonal Multiple Access (SOMA), Rate-adaptiveconstellation Expansion Multiple Access (EMA), Downlink Multiple User(DL MU), etc. The present disclosure is not limited to any of theafore-mentioned technologies, but has wide applicability to anysuperposition communication technology.

In general, multiple access superposition refers to communicating tomultiple users by linearly combining amplitude-weighted, encoded, and/ormodulated messages. For example, FIG. 1 has Base Station (BS) 110 (orevolved NodeB (eNB)) and two users (or User Equipments (UEs)), a near UE120 and a far UE 130 (“near” and “far” referring to their relativedistances from BS 110). Both the near UE 120 and the far UE 130 receivethe same signal x, comprising symbol x_(n) for the near UE 120 andsymbol x_(f) for far UE 130, which can be represented by Equation (1):

x=√{square root over (α_(N))}x _(N)+√{square root over (α_(F))}x_(F)  (1)

where α generally refers to transmission power, and thus α_(N) is thetransmission power allocated to the near user signal and α_(F) is thetransmission power allocated to the far user, where α_(N)+α_(F)=1.Sometimes a refers more generally to the ratio of near user power to faruser power, as shown in FIG. 2, which is discussed further below.

Speaking simplistically, near UE 120 decodes symbol x_(f) for far UE 130and uses it to cancel x_(f) as interference, thereby decoding symbolx_(n) intended for the near UE 120. One reiterative process for thistype of cancellation is “Successive Interference Cancellation” or SIC.The far UE 130, on the other hand, simply decodes its own signal x_(f).(although it is possible for the far user to also perform some form ofsignal cancellation to eliminate x_(n)).

Generally herein, far user symbol x_(F) corresponds to K_(F) bits ofdata represented as (d₀ ^(F)d₁ ^(F) . . . d_(K) _(F) ⁻¹ ^(F)) and nearuser symbol x_(N) corresponds to K_(N) bits of data represented as (d₀^(N)d₁ ^(N) . . . d_(K) _(N) ⁻¹ ^(N)).

FIG. 2 shows an example of a “super-constellation” formed of a (QPSK,QPSK) modulation pair under MUST. “(QPSK, QPSK)” means that both the farand near UE signals are modulated by QPSK. FIG. 2 is the result of adirect symbol mapping (DSM) of QPSK using Equation (1) for both the nearand far users, i.e., a 16-QAM (Quadrature Amplitude Modulation)super-constellation. Moreover, in FIG. 2, the constituent x_(f) andx_(n) symbols are separately Gray encoded.

Each of the four bit symbols in the 16-QAM super-constellation in FIG. 2comprises two bits for the symbol intended for the far user and two bitsof the symbol intended for the near user. More specifically, eachfour-bit symbol (b₀, b₁, b₂, b₃) comprises (b₀, b₁)=(d₀ ^(F)d₁ ^(F)),the two bits for the far user, and (b₂, b₃)=(d₀ ^(N)d₁ ^(N)), the twobits for the near user. Thus, the far user constellation is relativelycoarse, because each quadrant represents only one symbol (for example,the upper right quadrant is (00)), while each quadrant of the near userconstellation has all four symbols (00, 01, 10, and 11). However,because the near user is nearer, the near user's received signal isstronger and it will be easier for the near user to distinguish thatlevel of detail than the far user.

In theory, having the near user employ Successive InterferenceCancellation (SIC) by codeword, where the far user codeword is decoded,the original encoded far user codeword reconstructed using the decodedcodeword, and then the reconstructed original signal cancelled from theoverall signal prior to decoding, is optimal in the sense that itachieves capacity.

In practice, Code Word Interference Cancellation (CWIC), as describedabove, is rather difficult because the near user receiver needs to havethe far user's transmission parameters, such as, e.g., the codewordModulation and Coding Scheme (MCS), precoding matrix, rank, power boost,etc. If, for example, the network provided this information it wouldlead to an increase in control signaling overhead. In addition, thedecoding, re-constructing, and cancelling of the far user's codewordleads to a substantial usage of resources.

By contrast, Symbol-Level Interference Cancellation (SLIC) is alow-complexity approach and when joint detection, i.e., MaximumLikelihood (ML) detection, is used, SLIC can approach the performance ofCWIC in many scenarios. However, when SLIC is used, the log-likelihoodratio (LLR) distribution of the different bits in both symbols x_(N) andx_(F) can affect performance. For example, the direct symbol mapping(DSM) leads to degraded SLIC performance.

SUMMARY

Accordingly, the present disclosure has been made to address at leastthe problems and/or disadvantages described above and to provide atleast the advantages described below.

An aspect of the present disclosure provides a new type of superpositionsuper-constellation, the Gray-mapped Non-uniform Constellation (GNC).According to another aspect of the present disclosure, the spacingbetween neighboring symbols in the GNC super-constellation can beunequal. According to yet another aspect of the present disclosure, theGNC super-constellation is formed by a direct-sum of regularly spacedlattices, which leads to simplified joint LLR generation. According toanother aspect of the present disclosure, GNC can be easily extended forMUST with more than two users (i.e., more than simply a “near” and a“far” user).

According to one aspect of the present disclosure, a method is providedfor selecting a superposition constellation comprising two or more userequipment (UE) constellations. The method includes determining whichtype of superposition constellation (super-constellation) to generatebased at least on a power ratio among the two or more UEs, wherein onetype of super-constellation is a Gray-mapped Non-uniform-capableConstellation (GNC), in which both the constituent constellations of thetwo or more UEs and the GNC super-constellation itself are Gray-mapped;and when the determined type of superposition constellation is the GNCsuper-constellation, generating the determined type of superpositionconstellation by mapping the GNC super-constellation from outermost bitsto innermost bits according to each of K number of UEs.

According to another aspect of the present disclosure, an apparatus isprovided for selecting a superposition constellation comprising two ormore user equipment (UE) constellations. The apparatus includes at leastone non-transitory computer-readable medium storing instructions capableof execution by a processor; and at least one processor capable ofexecuting instructions stored on the at least one non-transitorycomputer-readable medium. The execution of the instructions results inthe apparatus performing a method comprising determining which type ofsuperposition constellation (super-constellation) to generate based atleast on a power ratio among the two or more UEs, wherein one type ofsuper-constellation is a Gray-mapped Non-uniform-capable Constellation(GNC), in which both the constituent constellations of the two or moreUEs and the GNC super-constellation itself are Gray-mapped; and when thedetermined type of superposition constellation is the GNCsuper-constellation, generating the determined type of superpositionconstellation by mapping the GNC super-constellation from outermost bitsto innermost bits according to each of K number of UEs.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features, and advantages of certainembodiments of the present disclosure will be more apparent from thefollowing detailed description, taken in conjunction with theaccompanying drawings, in which:

FIG. 1 is a diagram showing an example of Multi-User SuperpositionTransmission (MUST), with both a near UE and a far UE sharing asuperposed signal;

FIG. 2 is a super-constellation formed by direct symbol mapping (DSM) ofa (QPSK,QPSK) modulation pair for a far user and a near user; FIG. 3A isa super-constellation formed by Gray mapping a (QPSK,QPSK) modulationpair for a far user and a near user according to an embodiment of thepresent disclosure;

FIG. 3B is a super-constellation formed by Gray mapping a (QPSK,QPSK)modulation pair for a far user and a near user according to anembodiment of the present disclosure;

FIG. 4 is a conceptual diagram of a GNC signal generation apparatususing an M(⋅) function according to an embodiment of the presentdisclosure;

FIG. 5 is a conceptual diagram of a GNC signal generation apparatususing an N(⋅) function according to an embodiment of the presentdisclosure;

FIG. 6A is a flowchart illustrating the process of selecting andgenerating super-constellations according to various embodiments of thepresent disclosure; and

FIG. 6B a flowchart illustrating decision logic involved in theprocesses of scheduling, mapping, and modulation, according to anembodiment of the present disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE PRESENT DISCLOSURE

Hereinafter, embodiments of the present disclosure are described indetail with reference to the accompanying drawings. It should be notedthat the same elements will be designated by the same reference numeralsalthough they are shown in different drawings. In the followingdescription, specific details such as detailed configurations andcomponents are merely provided to assist the overall understanding ofthe embodiments of the present disclosure. Therefore, it should beapparent to those skilled in the art that various changes andmodifications of the embodiments described herein may be made withoutdeparting from the scope and spirit of the present disclosure. Inaddition, descriptions of well-known functions and constructions areomitted for clarity and conciseness. The terms described below are termsdefined in consideration of the functions in the present disclosure, andmay be different according to users, intentions of the users, orcustoms. Therefore, the definitions of the terms should be determinedbased on the contents throughout the specification.

The present disclosure may have various modifications and variousembodiments, among which embodiments are described below in detail withreference to the accompanying drawings. However, it should be understoodthat the present disclosure is not limited to the embodiments, butincludes all modifications, equivalents, and alternatives within thespirit and the scope of the present disclosure.

Although the terms including an ordinal number such as first, second,etc. may be used for describing various elements, the structuralelements are not restricted by the terms. The terms are only used todistinguish one element from another element. For example, withoutdeparting from the scope of the present disclosure, a first structuralelement may be referred to as a second structural element. Similarly,the second structural element may also be referred to as the firststructural element. As used herein, the term “and/or” includes any andall combinations of one or more associated items.

The terms used herein are merely used to describe various embodiments ofthe present disclosure but are not intended to limit the presentdisclosure. Singular forms are intended to include plural forms unlessthe context clearly indicates otherwise. In the present disclosure, itshould be understood that the terms “include” or “have” indicateexistence of a feature, a number, a step, an operation, a structuralelement, parts, or a combination thereof, and do not exclude theexistence or probability of addition of one or more other features,numerals, steps, operations, structural elements, parts, or combinationsthereof.

Unless defined differently, all terms used herein have the same meaningsas those understood by a person skilled in the art to which the presentdisclosure belongs. Such terms as those defined in a generally useddictionary are to be interpreted to have the same meanings as thecontextual meanings in the relevant field of art, and are not to beinterpreted to have ideal or excessively formal meanings unless clearlydefined in the present disclosure.

A related non-provisional patent application by the same inventors,entitled Power Allocation on Gray Mapped Superposition Transmission, isbeing filed concurrently, and claims priority to the same four U.S.provisional patent applications as does the present application. Thatapplication is expressly incorporated by reference in its entirety.

In general, it is preferable for a super-constellation to meet thefollowing three conditions:

(1) the super-constellation is Gray encoded/mapped;

(2) the balance of transmission power a can be arbitrarily set by theBS/eNB (i.e., having a non-uniform super-constellation, where points arenot equidistant); and

(3) the constellations making up the super-constellation are themselvesindividually Gray-encoded (this helps in a situation where the far UEhas a signal level close to the I+N floor).

The present disclosure describes a new type of super-constellation, aGray-mapped Non-uniform Constellation (GNC), a super-constellation whichis Gray encoded/mapped, allows the BS/eNB to select their own balance oftransmission power a among the users (i.e., non-uniform, but stillGray-mapped super-constellations), and ensures the constellations makingup the super-constellation are themselves individually Gray-encoded(i.e., in addition to the points of the super-constellation beingGray-mapped). This is discussed in Section I below.

Although named “Gray-mapped Non-uniform Constellation” (GNC), the term“GNC” covers both non-uniform and uniform super-constellations havingthe desirable characteristics. As such, “GNC” is sometimes also referredto herein as “Gray-mapped Non-uniform-capable Constellation”.

GNC is not always the optimal solution. There is an “exclusion” zonewhere using a GNC super-constellation may provide little or no benefitover other methods of mapping. Moreover, under certain power ratioconditions, better results can be found by “bit-swapping”-reversing thefar and near user bits within the GNC—as will be discussed in detailbelow. Accordingly, another aspect of the present disclosure is toprovide methodologies to determine the conditions under which a GNCshould be used, when bit-swapping should be used, and when neither ishelpful (and other methods may be used). See Sect. II below.

Moreover, another aspect of the present disclosure is to provide symboldetector options for MUST in general, and for bit-swapping GNC-basedsystems in particular. See Sect. III below. Similarly, yet anotheraspect of the present disclosure is to provide LLR generation/demappingoptions for MUST in general, and for bit-swapping GNC-based systems inparticular. See Sect. IV below. Lastly, control signaling for MUST ingeneral, and for bit-swapping GNC-based systems in particular, arediscussed as still another aspect of the present disclosure. See Sect. Vbelow.

I. Gray-Mapped Non-Uniform Constellation (GNC)

Below, methods for generating a Gray-mapped Non-uniform Constellation(GNC), are discussed, according to various embodiments of the presentdisclosure. Using this new type of bit-to-symbol mapping, Gray-mappingis ensured on both the user and super level, the spacing between symbolscan be unequal, and simplified joint LLR generation can be used becausethe GNC is formed by a direct-sum of regularly spaced lattices.Moreover, GNC can be easily extended to multiple users (i.e., more thansimply a “near” and a “far” user, as in most of the examples herein).

Generally speaking, using the simple example of one near and one faruser, where the constellation order of the near user is N_(n) and theconstellation order of the far user is N_(f), the super/jointconstellation is N_(s)=N_(n)*N_(f). For a standard uniform N_(s)-QAMconstellation, the real part of the analytical form can be presented asa simplified unit of the repeated nested form, disregarding the factorfor power normalization and preceding (1−2b₀) which is multiplied by therepeating nested structure, as shown in Equation (2):

$\begin{matrix}{\mspace{14mu} {\ldots \mspace{14mu}\left\lbrack {2^{({\frac{\log_{2}{({Ns})}}{2} - k})} - {\left( {1 - {2b_{2k}}} \right)\lbrack\mspace{14mu} \ldots \mspace{14mu}\rbrack}} \right\rbrack}} & (2)\end{matrix}$

where

$1 \leq k \leq {\frac{\log_{2}\left( N_{j} \right)}{2} - 1.}$

In a non-uniform N_(s)-QAM constellation according to embodiments of thepresent disclosure, new parameters q and p are used to balance thevarious interests in order to provide the GNC super-constellation, whereq guarantees the desired power split between the users and p relates tounit constellation power. One key factor is where to insert the factorof q in the nested structure so as to split the constellation and powerbetween near and far UEs. In an embodiment where the far UE takes theouter bits and near UE takes the inner bits, the q factor should beinserted at the following level in the nested structure as shown inEquation (3) below:

$\begin{matrix}{\mspace{14mu} {\ldots \mspace{14mu}\left\lbrack {2^{\frac{\log_{2}{(N_{n})}}{2}} - {{q\left( {1 - {2b_{\log_{2}{(\frac{N_{s}}{N_{n}})}}}} \right)}\lbrack\mspace{14mu} \ldots \mspace{14mu}\rbrack}} \right\rbrack}} & (3)\end{matrix}$

As mentioned above, new parameter q is designed to maintain Gray mappingin joint/super constellations between two or more UEs in light of thespecific power constraints and/or desired power conditions.

A specific example is presented in the section below.

A. (QPSK, QPSK) Example of a Nested Constellation Structure

In this section, a (QPSK,QPSK) modulation pair mapping to a 16-QAMsuper-constellation, like FIG. 2, will be presented in FIGS. 3A and 3Baccording to embodiments of the present disclosure. Also like FIG. 2,each four-bit (“super”)-symbol (b₀, b₁, b₂, b₃) comprises two far userbits, (b₀, b₁)=(d₀ ^(F)d₁ ^(F)), and two near users bits, (b₂,b₃)=(d₀^(N)d₁ ^(N)).

The mappings in FIGS. 3A and 3B are different from FIG. 2. The far userbits still have the same pattern of values as FIG. 2, with (10) for theupper-left quadrant of the super-constellation, (00) for the upper-rightquadrant, (01) for the lower-right quadrant, and (11) for the lower leftquadrant. However, near user bits (b₂, b₃) define Gray labeledconstellation points with each set for a given value of the pair (b₀,b₁). In other words, the pairs of bits (b₀, b₁) and (b₂, b₃) form anested structure where (b₀, b₁) constitute the “outer” part of thedirect sum and (b₂, b₃) form the “inner” part of the direct sum, asshown in Equation (4)(a).

$\begin{matrix}{\left( {b_{0},b_{1},b_{2},b_{3}} \right) = {\underset{({{outer}\mspace{14mu} {part}})}{\left( {b_{0},b_{1}} \right)} \oplus \underset{({{inner}\mspace{14mu} {part}})}{\left( {b_{2},b_{3}} \right)}}} & {(4)(a)}\end{matrix}$

Without loss of generality, α_(F)>α_(N)=1−α_(F) or, equivalently,α_(F)>0.5 is assumed (generally, it is expected that the larger fractionof power is allocated to the far user in NOMA; if this is not the case,the roles of α_(F) and α_(N) can be swapped-so this assumption is notrestrictive).

Furthermore, the unequal power split can be made part of the symbolmapping process using new parameters q and p as shown in Equations(4)(b) and (4)(c) below:

$\begin{matrix}{x = {\frac{1}{\sqrt{C}}\left\{ {{{p\left( {1 - {2b_{0}}} \right)}\left\lbrack {2 - {q\left( {1 - {2b_{2}}} \right)}} \right\rbrack} + {{{jp}\left( {1 - {2b_{1}}} \right)}\left\lbrack {2 - {q\left( {1 - {2b_{3}}} \right)}} \right\rbrack}} \right\}}} & {(4)(b)}\end{matrix}$

which is the same as

$\begin{matrix}{x = {\frac{1}{\sqrt{C}}\left\{ {{{p\left( {1 - {2d_{0}^{F}}} \right)}\left\lbrack {2 - {q\left( {1 - {2b_{0}^{N}}} \right)}} \right\rbrack} + {{{jp}\left( {1 - {2d_{1}^{F}}} \right)}\left\lbrack {2 - {q\left( {1 - {2d_{1}^{N}}} \right)}} \right\rbrack}} \right\}}} & {(4)(c)}\end{matrix}$

where p and q are positive real-valued numbers as discussed above and Cis a power constraint value to normalize the power of symbols on thejoint constellation map.

FIG. 3A shows a (QPSK,QPSK) modulation pair mapping to a 16-QAMsuper-constellation, using the values of p=0.9354 and q=1.3093,equivalent to α_(N)=0.3 and α_(F)=0.7, according to an embodiment of thepresent disclosure. The distances between constellation points/symbolsare clearly not uniform.

While Equations (4)(b)/(c) provide the general mapping formula for a(QPSK,QPSK) modulation pair mapping to a non-uniform 16-QAMsuper-constellation, they also include a uniform 16-QAMsuper-constellation according to an embodiment of the present disclosureas a special case. Namely, setting the values p=q=1 or equivalentlyα_(F)>0.8 results in a uniform 16-QAM super-constellation with theunique inner/outer qualities according to an embodiment of the presentdisclosure.

Accordingly, FIG. 3B shows a (QPSK,QPSK) modulation pair mapping to a16-QAM super-constellation, using the values of p=1 and q=1, equivalentto α_(N)=0.2 and α_(F)=0.8, according to an embodiment of the presentdisclosure. In this special case of the more general GNC mappingequations, the distances between constellation points/symbols areuniform.

3GPP RAN1 has established scenarios to evaluate implementations of MUST(i.e., superposition systems). Initially, only two scenarios were used:“Scenario 1”, a one-layer or scalar environment and “Scenario 2”, amulti-layer environment where a rank 2 precoded signal is transmitted tothe near user while a rank 1 slightly differently precoded signal istransmitted to the far user. For more details regarding the scenarios,see, for example, the four U.S. provisional patent applications fromwhich the present application claims priority which have also beenexpressly incorporated by reference.

To meet those scenarios, p and q of the 16-QAM (QPSK,QPSK)super-constellation are subject to certain constraints. For Scenario 1(scalar/one-layer superposition), the constraints are:

1) 2p²(4+q²)=C which arises from unit constellation power; and

${{\left. 2 \right)\mspace{14mu} \frac{q^{2}}{4}} = \frac{1 - \alpha_{F}}{\alpha_{F}}},$

which arises from the power split requirement between (b₀, b₁) bits and(b₂, b₃) bits.

For Scenario 2 (two-layer superposition), the constraints are:

${\left. {{{{\left. 1 \right)\mspace{14mu} 2{p^{2}\left( {4 + q^{2}} \right)}} = {0.5{C\left( {1 + \alpha_{F}} \right)}}};{and}}2} \right)\mspace{14mu} \frac{q^{2}}{4}} = {\frac{1 - \alpha_{F}}{2\alpha_{F}}.}$

The constellation that x belongs to is denoted as S_(p,q)(X_(QPSK),X_(QPSK)) since it is formed from underlying (QPSK,QPSK) constellationsand parameterized by p, q. In the above, p can always be set equal to 1since it is scaled out by the normalization factor C. Thus, according toan embodiment of the present disclosure, the nonlinear mapping of theform x=f_(p,q)(x₀, x₁) is defined, which results in a Gray-mappedNon-uniform Constellation, also known as GNC. A mentioned above, theconventional 16-QAM constellation is a special type of GNC, i.e., whenp=q=1.

Since selective “companding” (i.e., compression and expansion ofdifferent sets of constellation points) was applied to a Gray encodedconstellation above, it is easy to verify that the bit labelingresulting from Equations (4)(b)/(c) above is also Gray. Any two adjacentsymbols of the super-constellation differ by only one bit because theunder-lying constellation is Gray encoded.

Moreover, as can be seen in FIGS. 3A and 3B, in the four symbols in thecenter, the near user bits do not change (i.e., they are all “00”) whilethe far user bits do. This is in contrast with FIG. 2 (i.e., directsymbol mapping), where both the near and far bits in the four centersymbols change per symbol.

While the (QPSK, QPSK) 16-QAM super-constellation is provided as anexample above, additional super-constellations can be generated in thesame manner. For example, the specific equations and constraints for thesuper-constellations shown in Table 1 below are provided in the APPENDIXI appended hereto, as well as in U.S. Prov. Pat. App. Ser. Nos.62/173,241 and 62/203,818, from which the present application claimspriority (and which have been incorporated by reference in theirentirety).

TABLE 1 Resulting “Far” UE constellation “Near” UE constellation“Super-constellation” (2^(K) _(F))-QAM (2^(K) _(N))-QAM (2^(K)_(F)+K_(N))-QAM QPSK QPSK 16QAM 16QAM QPSK 64QAM QPSK 16QAM 64QAM 16QAM16QAM 256QAM 64QAM QPSK 256QAM QPSK 64QAM 256QAM 64QAM 16QAM 1024QAM16QAM 64QAM 1024QAM 64QAM 64QAM 4096QAM.

B. General Mapping for Arbitrary Constellation Pairs

The approach above can be extended to any arbitrary combination ofconstituent constellations. Like before, the “near” UE and “far” UE areinter-changeable. The “far” user's bits are mapped to the outer part ofthe resultant constellation and the near user's bits are mapped to theinner part of the resultant constellation. As a result, the bit mappingfor (QPSK,16QAM) is not the same as that for (16QAM,QPSK), for example.

When viewed more generally, the outer bits (mapped to the far user inthe above example) can be viewed as the “base layer” and the inner bits(mapped to the near user in the above example) can be viewed as the“extension layer”.

(1) General GNC Equation Using M(⋅) Function

Accordingly, the generally-applicable GNC equation can be written as alinear combination of the base layer (x_(F)) and a function of the baselayer and extension layer (x_(N)), as set forth in Equation (5):

$\begin{matrix}{x = {\frac{p}{\sqrt{C}}\left\{ {{ax}_{F} + {q\left( {{{M\left( {d_{0}^{F}d_{2}^{F}\mspace{14mu} \ldots \mspace{14mu} d_{K_{F} - 2}^{F}} \right)}{Re}\left\{ x_{N} \right\}} + {{{jM}\left( {d_{1}^{F}d_{3}^{F}\mspace{14mu} \ldots \mspace{14mu} d_{K_{F} - 1}^{F}} \right)}{Im}\left\{ x_{N} \right\}}} \right)}} \right\}}} & (5)\end{matrix}$

where a is a factor that depends on the modulation orders and M(d₀^(F)d₂ ^(F) . . . d_(K) _(F) ⁻² ^(F)) and M(d₁ ^(F)d₃ ^(F) . . . d_(K)_(F) ⁻¹ ^(F)) represent the function M(⋅) applied to the even and oddbits of the base layer X_(F) respectively.

Function M(⋅) takes only the values of −1 and +1. As a result, the Iand/or Q values of the extension layer symbol x_(N) undergo signinversions (equivalent to reflections of the constellation) after themapping of data bits {d₀ ^(N) . . . d_(K) _(N) ⁻¹ ^(N)} to a (2^(K)_(N))-QA constellation prior to transmission.

The function M(d₀d₁ . . . d_(K-1)) is summarized for the differentmodulation order pairs in Table 2 below.

TABLE 2 a and M(•) for Different Modulation Pairs - (FIG. 4) “Far”“Near” UE Resulting “Super- UE constellation constellationconstellation” (2^(K) _(F))-QAM (2^(K) _(N))-QAM (2^(K) _(F)+K_(N))-QAMa M(d₀d₁ . . . d_(K−1)) QPSK QPSK 16-QAM 2 −(1 − 2d₀) 16-QAM QPSK 64-QAM2 (1 − 2d₀)(1 − 2d₁) QPSK 16-QAM 64-QAM 4 −(1 − 2d₀) 16-QAM 16-QAM256-QAM 4 (1 − 2d₀)(1 − 2d₁) 64-QAM QPSK 256-QAM 2 −(1 − 2d₀)(1 − 2d₁)(1− 2d₂) QPSK 64-QAM 256-QAM 8 −(1 − 2d₀) 64-QAM 16-QAM 1024-QAM 4 −(1 −2d₀)(1 − 2d₁)(1 − 2d₂) 16-QAM 64-QAM 1024-QAM 8 (1 − 2d₀)(1 − 2d₁)64-QAM 64-QAM 4096-QAM. 8 −(1 − 2d₀)(1 − 2d₁)(1 − 2d₂)

FIG. 4 is a conceptual diagram of a GNC signal generation apparatus forgenerating a GNC signal in accordance with Equation (5) above, using theM(⋅) function and assuming that the far user bits are mapped to the baselayer, according to an embodiment of the present disclosure.

As shown in FIG. 4, all of the far user bits (d₀ ^(F)d₁ ^(F) . . . d_(K)_(F) ⁻¹ ^(F)) are input to M-QAM mapper 410, while at the same time theeven bits of the far user bits are input into M(⋅) module 413 and theodd bits of the far user bits are input into M(⋅) module 415. The M-QAMmapper 410 performs the function of mapping the far user bits, therebyproducing the far user signal which is subsequently power scaled by pa

$\frac{pa}{\sqrt{C}}$

at 450 before being mixed with the near user signal at 460 to producethe GNC symbol output. On the other hand, M(⋅) module 413 performs theM(⋅) function on the far user even bits and M(⋅) module 415 performs theM(⋅) function on the far user odd bits, which are used in generating thenear user signal, as discussed below.

All of the near user bits {d₀ ^(N) . . . d_(K) _(N) ⁻¹ ^(N)} are inputto M-QAM mapper 420, which, similarly to M-QAM mapper 410, performs thefunction of mapping the near user bits. The output of M-QAM mapper 420is input to both the Re(⋅) module 423, which creates the real part ofthe signal, and the Im(⋅) module 425, which creates the imaginary partof the signal.

The output of M(⋅) module 415 is mixed with the output of Im(⋅) module425 and the imaginary value j at 435. Similarly, the output of M(⋅)module 413 is mixed with the output of Re(⋅) module 423 at 433. Thosemixed outputs are themselves mixed at 430 to produce the near userportion of the signal, which undergoes power scaling by being mixed with

$\frac{pq}{\sqrt{C}}$

at 440 before being mixed with the far user signal at 460 to produce theGNC symbol output.

The present disclosure is not limited to the linear combination shown inEquation (5) and generated in FIG. 4 but rather can take a number offorms. Accordingly, a signal generation technique and signal generationapparatus according to another embodiment are described below.

(2) General GNC Equation Using N(⋅) Function

More specifically, FIG. 5 is a conceptual diagram of a signal generationapparatus using bit-level operations and an N(⋅) function, where thegenerally applicable GNC equation for FIG. 5 is written as set forth inEquation (6):

$\begin{matrix}{x = {\frac{p}{\sqrt{C}}\left\{ {{ax}_{F} + {qx}_{N}^{\prime}} \right\}}} & (6)\end{matrix}$

where a is a factor that depends on the modulation orders, like in Eq.(5), and x′_(N) is the M-QAM constellation that corresponds to the bitsequence {c₀, c₁, . . . c_(K) _(F) ⁻¹}, where:

{c ₀ ,c ₂ , . . . ,c _(K) _(F) ⁻² }={e ₀ ⊕d ₀ ^(N) ,e ₀ ⊕d ₂ ^(N) , . .. ,e ₀ ⊕d _(K) _(F) ⁻² ^(N)}  (7)(a)

{c ₁ ,c ₃ , . . . ,c _(K) _(F) ⁻¹ }={e ₁ ⊕d ₁ ^(N) ,e ₁ ⊕d ₃ ^(N) , . .. ,e ₁ ⊕d _(K) _(F) ⁻¹ ^(N)}  (7)(b)

and

e ₀ =N(d ₀ ^(F) ,d ₂ ^(F) , . . . d _(K) _(F) ⁻² ^(F))  (8)(a)

e ₁ =N(d ₁ ^(F) ,d ₃ ^(F) , . . . d _(K) _(F) ⁻¹ ^(F))  (8)(b)

The N(⋅) function takes only the binary values of 0 and 1 and thefunction N(d₀d₁ . . . d_(K-1)) is summarized for the differentmodulation order pairs in Table 3 below.

TABLE 3 a and N(•) for Different Modulation Pairs - (FIG. 5) “Far” UE“Near” UE Resulting “Super- constellation constellation constellation”(2^(K) _(F))-QAM (2^(K) _(N))-QAM (2^(K) _(F)+K_(N))-QAM a N(d₀d₁ . . .d_(K−1)) QPSK QPSK 16-QAM 2 1 ⊕ d₀ 16-QAM QPSK 64-QAM 2 d₀ ⊕ d₁ QPSK16-QAM 64-QAM 4 1 ⊕ d₁ 16-QAM 16-QAM 256-QAM 4 d₀ ⊕ d₁ 64-QAM QPSK256-QAM 2 1 ⊕ d₀ ⊕ d₁ ⊕ d₂ QPSK 64-QAM 256-QAM 8 1 ⊕ d₀ 64-QAM 16-QAM1024-QAM 4 1 ⊕ d₀ ⊕ d₁ ⊕ d₂ 16-QAM 64-QAM 1024-QAM 8 d₀ ⊕ d₁ 64-QAM64-QAM 4096-QAM. 8 1 ⊕ d₀ ⊕ d₁ ⊕ d₂

As stated above, FIG. 5 is a conceptual diagram of a GNC signalgeneration apparatus for generating a GNC signal in accordance withEquation (6) above, using the N(⋅) function and assuming that the faruser bits are mapped to the base layer, according to an embodiment ofthe present disclosure.

As shown in FIG. 5, all of the far user bits (d₀ ^(F)d₁ ^(F) . . . d_(K)_(F) ⁻¹ ^(F)) are input to M-QAM mapper 510, while at the same time theeven bits in the far user bits are input into N(⋅) module 513 and theodd bits in the far user bits are input into N(⋅) module 515. The M-QAMmapper 510 performs the function of mapping the far user bits, therebyproducing the far user signal which is subsequently power scaled by

$\frac{pa}{\sqrt{C}}$

at 550 before being mixed with the near user signal at 560 to producethe GNC symbol output. On the other hand, N(⋅) module 513 performs theN(⋅) function on the far user even bits, producing e₀, and N(⋅) module515 performs the N(⋅) function on the far user odd bits, therebyproducing e₁, which are used in generating the near user signal, asdiscussed below.

On the other hand, the near user bits {d₀ ^(N) . . . d_(K) _(N) ⁻¹ ^(N)}are split into its even bits, which are input to Bit XOR module 522, andits odd bits, which are input to Bit XOR module 524. Bit XOR module 522and Bit XOR module 524 also receive e₀, and e₁ as input from N(⋅) module513 and N(⋅) module 515, respectively. Thus, Bit XOR module 522 performsthe XOR operation on the even near user bits and e₀ and Bit XOR module524 performs the XOR operation on the even near user bits and e₁. Theeven XOR′d bits from Bit XOR module 522 and the odd XOR′d bits from BitXOR module 524 are both input into M-QAM mapper 520, which converts theseries of both even and odd bits to a QAM symbol.

The output of M-QAM mapper 520, comprising x′_(N), undergoes powerscaling by being mixed with

$\frac{pq}{\sqrt{C}}$

at 540 before being mixed with the far user signal at 560 to produce theGNC symbol output.

C. Extension to More than Two Users

In yet another related embodiment of the present disclosure, the Graymapping method can be extended to more than two users, i.e., a K-usersystem.

Information symbols of K users can be linearly superposed to yieldEquation (9):

x=√{square root over (α₀)}x ₀+√{square root over (α₁)}x ₁+ . . .+√{square root over (α_(K-1))}x _(K-1)  (9)

where x_(j) is the M-QAM symbol for the j-th user such that α_(j)>0 andthe constraint α₀+α₁+ . . . +α_(K-1)=1 holds.

When, for example, the K=2, the signal received at a given user'sreceiver can be written as Equation (10) below:

y=h(√{square root over (α_(N))}x ₀+√{square root over (α_(F))}x₁)+n  (10)

where y=[y₀, . . . , y_(n) _(R−1) ]^(T) is a n_(R)×1 receive signalvector, h is the n_(R)×1 channel vector (which includes precoding at theeNB, if any), and n is the vector that models additive white Gaussiannoise (AWGN) which has the distribution CN(0, σ_(n) ²l).

The bits for the K users can be mapped as a super-constellation fromoutermost bits to innermost bits of the super-constellation. Thesuper-constellation is Gray encoded when some conditions on α_(j) aresatisfied. For example, if all K users have QPSK as their single-userconstellations, the mapping can be written as Equation (11):

(b ₀ ,b ₁ ,b ₂ ,b ₃ , . . . ,b _(2k-2) ,b _(2K-2))=(b ₀ ,b ₁)⊕(b ₂ ,b ₃). . . ⊕(b _(2K-2) ,b _(2K-1))  (11)

leading to a (2^(2K))-QAM super-constellation. For example, for K=3,this approach leads to bits-to-symbol mapping defined by Equation (12):

$\begin{matrix}{x = {\frac{1}{\sqrt{C}}\left\{ {{\left( {1 - {2d_{0}^{(0)}}} \right){p\left\lbrack {4 - {{q\left( {1 - {2d_{0}^{(1)}}} \right)}\left\lbrack {2 - {r\left( {1 - {2d_{0}^{(2)}}} \right)}} \right\rbrack}} \right\rbrack}} + {{j\left( {1 - {2d_{1}^{(0)}}} \right)}{p\left\lbrack {4 - {{q\left( {1 - {2d_{1}^{(1)}}} \right)}\left\lbrack {2 - {r\left( {1 - {2d_{3}^{(2)}}} \right)}} \right\rbrack}} \right\rbrack}}} \right\}}} & (12)\end{matrix}$

where (d₀ ^((j))d₁ ^((j))) refers to the bits of the j-th user, and p,q, and r are positive real-valued numbers which, in Equation (12), aresubject to the constraint indicated by Equation (13):

2p ²(16+4q ² +q ² r ²)=C  (13)

It is trivial to extend the above to the case of arbitrary combinationsof modulation orders for the K users.

As shown above, a new type of bit-to-symbol mapping produces a new typeof super-constellation, the Gray-mapped Non-uniform Constellation, orGray-mapped Non-uniform-capable Constellation, (GNC). Several methodsfor providing such mapping are described and it is shown that it can beextended to any arbitrary number of users (i.e., more than simply a“near” and a “far” user).

II. Adaptive Scheduling/Mapping Using GNC

A. Adaptive Bit Swapping to Maintain Gray Mapping

According to an embodiment of the present disclosure, adaptive bitmapping can be used to maintain Gray mapping, irrespective of therelative powers of the far user and the near user.

In the GNC mapping described above, certain conditions need to bemaintained. For example, in order for Gray mapping to be maintained in a(QPSK, QPSK) super-constellation, the condition q<2 needs to besatisfied. The same condition needs to be met for (16QAM, QPSK) and(64QAM, QPSK) super-constellations. Similarly, the condition 3q<4 needsto be satisfied for the (QPSK, 16QAM) and (16QAM, 16QAM)super-constellations. For (QPSK, 64QAM), the condition 7q<8 needs to besatisfied.

Accordingly, the power ratio

$\frac{\alpha_{N}}{\alpha_{F}} = {\frac{1 - \alpha_{F}}{\alpha_{F}} < T}$

for Scenario 1 and the power ratio

$\frac{\alpha_{N}/2}{\alpha_{F}} = {\frac{1 - \alpha_{F}}{2\alpha_{F}} < T}$

for Scenario 2 must be satisfied for the values of T given by Table 4below.

TABLE 4 Necessary Conditions for Maintenance of Gray Mapping (far, near)Modulation pair T (QPSK, QPSK) 1 (16-QAM, QPSK) 1/5 (QPSK, 16-QAM) 5/9(16-QAM, 16-QAM) 1/9 (64-QAM, QPSK) 1/21 (QPSK, 64-QAM) 3/7 (64-QAM,16-QAM) TBD (16-QAM, 64-QAM) TBD (64-QAM, 64-QAM) TBD

When the above power ratio conditions are not met, direct mapping leadsto a non-Gray mapping. However, Gray mapping is still possible, if theroles of the near and far users are swapped, i.e., the outer bits can beassigned to the near user and the inner bits can be assigned to the faruser, leading to near user bits (b₀, b₁, . . . )=(d₀ ^(N), d₁ ^(N), . .. ) and far user bits (b_(2k), b_(2k+1), . . . )=(d₀ ^(F), d₁ ^(F), . .. ).

TABLE 5 GNC Exclusion Region for Gray${Mapping}\mspace{14mu} {based}\mspace{14mu} {on}\mspace{14mu} \frac{\alpha_{N}}{\alpha_{F}}\mspace{14mu} {ratio}$(far, near) Modulation pair Scenario 1 Scenario 2 (QPSK, QPSK) null setnull set (16-QAM, QPSK) (1/5, 9/5) (2/5, 18/5) (QPSK, 16-QAM) (5/9, 5)(10/9, 10) (16-QAM, 16QAM) (1/9, 9) (2/9, 18) (64-QAM, QPSK) (1/21, 7/3)(2/21, 14/3) (QPSK, 64-QAM) (3/7, 21) (6/7, 42) (64-QAM, 16-QAM) TBD TBD(16-QAM, 64-QAM) TBD TBD (64-QAM, 64-QAM) TBD TBD

The above condition can be equivalently written as:

-   -   α_(F)>T₁ (Gray mapping without bit swapping)    -   α_(F)<T₂ (Gray mapping with swapping)

The exclusion region is defined with respect to α_(F) as (T₁, T₂), forsuitable real numbers T₁, T₂ such that 0<T₂<T₁<1.

When the conditions for Gray mapping are not met due to power allocationat the scheduler, there are two options:

-   -   Option 1: Maintain GNC mapping    -   Option 2: Fall back to direct symbol mapping

Even when the conditions for Gray mapping are violated, there arecertain scenarios (certain pairs of MCS and power ratio) where GNCoutperforms DSM.

In this embodiment, Gray mapping is used whenever feasible, byadaptively selecting GNC or DSM as follows:

-   -   if α_(F)>t₀ use GNC with no swapping and mapping far user bits        to outer bits and    -   if α_(F)<t₁ use GNC with bit swapping and mapping far user bits        to inner bits,    -   if t₁<α_(F)<t₀, use DSM

where t₀ and t₁ are two thresholds, such that t₁≤t₀. The thresholds t₀and t₁ need to be selected based on the MCS pair being used for the twousers. For many constellation pairs (lower order QAM), either GNCwithout swapping or GNC with swapping is better than DSM for any α_(F),thus, t₀=t₁. For other constellation pairs (mainly higher order QAM),there is a small region within t₁<α_(F)<t₀ where DSM outperforms GNC.

There may also be some benefit in transitioning to bit swapping either a“little early” as, for example, α_(F) increases for trading off far userperformance for near user performance, or a “little late”, as, forexample, α_(N) increases for trading off near SNR for far user SNR. Forexample, for (QPSK, QPSK) a threshold may be chosen to be slightlysmaller than for 1 (instead of exactly 1) for bit swapping. As anotherexample, for (QPSK, QPSK) a threshold t₀ to be smaller that 0.5 (insteadof exactly 0.5) for bit swapping. The thresholds can be modified basedon the user MCS selected.

In addition to the relative powers allocated by the scheduler for thenear user and the far user and the user rank, the near user MCS and thefar user MCS also need to be taken into account in order to determinewhether the outer bits should be mapped to the far user or the nearuser. Bit swapping leads to a different minimum distance for near (far)user symbols compared to no swapping. Accordingly, the target BlockError Rate (BLER) is a function of both the bit mapping order (i.e., noswapping vs. bit swapping) and the relative power allocation for the twousers (and additionally the transmission rank for the two users).

In general, the scheduler needs to determine the target rates achievablefor both no-swapping and bit-swapping options based on the minimumdistance (for near and far user symbols in the super-constellation)achieved with either option. The largest MCS pair that can achieve acertain target BLER level with no-swapping may be different from thelargest MCS pair that can achieve the same target BLER level withbit-swapping.

Accordingly, the scheduler needs to jointly perform:

-   -   1. user pair selection,    -   2. decision to transmit using MUST vs. use single user        transmission on an RB or set of RBs    -   3. MUST transmission configuration        -   a. transmission rank        -   b. power split among users/power split selection        -   c. user MCS pair for MUST,        -   d. selection of (i) GNC w/swap; (ii) GNC w/o swap; and (iii)            DSM.

The selection can be made jointly in order to maximize weighted sumrate, packet flow (PF) metric, and other parameters at the scheduler.

Therefore, the bit-swapping criterion can be formulated as any one ofthe options below, i.e., bit-swapping is performed if any one ofEquations (14)(i) through (14)(v) is met:

$\begin{matrix}{{f_{1}\left( {\alpha_{N},\alpha_{F},r_{N},r_{F},{MCS}_{N},{MCS}_{F}} \right)} < T_{1}} & {(14)(i)} \\{{f_{2}\left( {\alpha_{N},\alpha_{F},r_{N},r_{F},{MCS}_{N},{MCS}_{F}} \right)} < {T_{2}\left( {m_{N},m_{F}} \right)}} & {(14)({ii})} \\{{f_{3}\left( {\frac{\alpha_{N}}{\alpha_{F}},r_{N},r_{F},{MCS}_{N},{MCS}_{F}} \right)} < {T_{2}\left( {m_{N},m_{F}} \right)}} & {(14)({iii})} \\{{f_{4}\left( {{\frac{\alpha_{N}}{\alpha_{F}}{MCS}_{N}},{MCS}_{F}} \right)} < {T_{3}\left( {m_{N},m_{F},r_{N},r_{F}} \right)}} & {(14)({iv})} \\{{f_{5}\left( \frac{\alpha_{N}}{\alpha_{F}} \right)} < {T_{4}\left( {m_{N},m_{F},r_{N},r_{F},{MCS}_{N},{MCS}_{F}} \right)}} & {(14)(v)}\end{matrix}$

Here:

-   -   f₁, f₂, f₃, f₄, f₅ are various mapping functions;    -   T₁ is a threshold;    -   T₂, T₃ and T₄ are threshold functions;    -   MCS_(N), MCS_(F) are MCSs for the near user and far user        respectively (this implicitly includes modulation information);    -   m_(N), m_(F) are modulation orders for the near user and far        user respectively (these are dependent on the selected MCS_(N),        MCS_(F); and    -   r_(N), r_(F) are transmission ranks for the near user and far        user respectively.

When a GNC scheme is used, the “no-swapping” vs. “bit-swapping”selection problem is a part of the scheduler implementation where thescheduler jointly performs user selection and MUST vs. no MUSTselection, and if MUST is employed, the scheduler performs user MCSpair, rank, and power split selection.

If either user has a rank 2 transmission, the user MCS can be replacedwith the user MCS pair for the two layers. For example, for Scenario 2,MCS_(N) can be replaced with the pair (MCS_(N,1), MCS_(N,2)), whichdenotes the MCS for the two layers in the above-described thresholdcriteria.

FIG. 6A is a flowchart illustrating the process of selecting andgenerating super-constellations according to various embodiments of thepresent disclosure. FIG. 6A is a simplistic representation of the mainoperations and factors involved.

In 610A, the parameters used to make the following decisions arereceived, collected, and/or generated, such as, for example, the a powerratio. In 620A, the type of super-constellation to use is determined,based on the parameters of 610A. Finally, in 630A, the bits of the Kusers are mapped to the super-constellation of the determined type.

FIG. 6B is a flowchart illustrating decision logic involved in theprocesses of scheduling, mapping, and modulation, according to anembodiment of the present disclosure. In other words, FIG. 6B fills insome of the details and examples involved in an implementation of FIG.6A. FIG. 6B is a simplistic representation of what would be implementedas a number of interacting processes and subroutines and is being usedfor purposes of explanation only.

In 610B, data needed to make the following decisions are received,including, but not limited to, one or more of the α_(N)/α_(F) powerratio, the far user MCS, the near user MCS, the far user Multiple InputMultiple Output (MIMO) rank, the near user MIMO rank, target BLER,target throughput, and similar possibly pertinent parameters, as wouldbe known to one of ordinary skill in the art.

In 620B, the selection, based at least in part on the data received in610A, is made among:

-   -   GNC with no swapping;    -   GNC with swapping; and    -   DSM.

The scheduler/modulation mapper determines whether the criterion passesbased on the received elements. When the criterion passes, thescheduler/modulation mapper maps outer bits to the far user and mapsinner bits to the near user. When the criterion does not pass, thescheduler/modulation mapper maps outer bits to the near user and mapsinner bits to the far user.

If GNC with no swapping is selected in 620B, the outer bits are mappedto the far user: (b₀,b₁, . . . )=(d₀ ^(F),d₁ ^(F), . . . ), and theinner bits are mapped to the near user: (b_(2K),b_(2K+1) . . . )=(d₀^(N), d₁ ^(N), . . . ), i.e., no bit swapping, in 630B-a.

If GNC with swapping is selected in 620B, the inner bits are mapped tothe far user: (b_(2K), b_(2K+1), . . . )=(d₀ ^(F),d₁ ^(F), . . . ), andthe outer bits are mapped to the near user: (b₀,b₁, . . . )=(d₀ ^(N),d₁^(N), . . . ), i.e., the far and near bits have swapped inner-outer, in630B-13.

If DSM is selected in 620B, the far user's bits (d₀ ^(F),d₁ ^(F), . . .) and the near user's bits (d₀ ^(N), d₁ ^(N), . . . ) are directlymapped in 630B-γ.

When the bits are swapped before transmission, three detectors arefeasible, as set forth below.

-   -   1) Full joint LLR generation—for this option, either Log-MAP        (Maximum A Posteriori) (best performance) or Max-Log-MAP can be        used to generate LLRs for both near and far user bits;    -   2) Perform hard slicing of the near user first treating the far        user as noise, then symbol SIC to remove the near user        interference, and then generate far user LLR; and    -   3) Treating the near user as noise and perform SU detection on        far user data.

While the third option is simplest, it will have poor performance. Thefirst option has the best performance but involves determining an LLRfor the bits of the super-constellation.

III. MUST Detector

There are several symbol detector options for MUST. For joint demapping,both x_(F) and x_(N) are jointly demapped by both far and near UEs(i.e., independent of the UE near/far condition). The UE will need toimplement up to 4096-QAM soft demapper even if only {QPSK, 16-QAM,64-QAM} are allowed as the single-user constellations. Details for softdemapping of non-uniform M-QAM constellation (M<=4096) are described ingreater detail below. The rank 1 (rk1) Log-MAP (direct method or usingrk2 LM) approach can be used for this case. The UE will need toimplement up to 65,536-QAM soft demapper if {QPSK, 16-QAM, 64-QAM,256-QAM} are all allowed as single-user constellations. The rk2 DL-LMapproach is used for computing LLR. Further details on rk2 LM with SICor turbo-detection/decoding (Turbo-DD) when feasible for the non-uniformconstellation are described in greater detail below.

For Hybrid SU detection and SIC based on a UE near/far condition, thenear UE detects both x_(F) and x_(N). The UE uses successiveinterference cancellation (SIC) where x_(F) is first detected (treatingx_(N) as noise) and cancelled followed by detection of x_(N). The far UEalways performs SU detection of x_(F) (treating x_(N) as noise). A UEdetermines if it is a near UE or a far UE based on measurements, e.g.,reference signal received quality (RSRQ) or reference signal receivedpower (RSRP) levels, or some other control information. This hybrid SUdetection option outperforms joint demapping.

As mentioned above, there are three (3) options for lower complexity faruser detection. The first option is the conventional detector anddecoding. The near user is treated as noise and SU detection isperformed on far user data. Although it is the simplest, the firstoption has poor performance as the near user maps to outer bits, whichis highly non-Gaussian. The second option is Symbol-level IC (SLIC). Thesecond option is a feasible option. For full joint LLR generation,either Log-MAP (best performance) or Max-Log-MAP can be used to generateLLRs for both near and far user bits. Hard slicing of the near user isperformed first treating the far user as noise. Symbol SIC is thenperformed to remove near user interference and then generate far userLLR. The third option is CW-level IC (CWIC). Generally, the near userMCS is expected to be high and the SINR conditions at the far user maybe insufficient to decode the near user CW even with side information.Thus, CWIC is likely infeasible.

The different detector options for near and far users are described ingreater detail below.

A. Scalar/1-Layer Superposition

With respect to scalar or 1-layer superposition, the received signal canbe written as Equation (15):

y=h(√{square root over (α)}x ₀+√{square root over (1−α)}x′ ₀)+n  (15)

where y=[y₀, . . . , y_(n) _(R) ⁻¹]^(T) is a n_(R)×1 receive signalvector, x₀ belongs to (2^(K) ¹ )-QAM constellation which is the datasymbol of interest and x′₀ belongs to (2^(K) ² )-QAM constellation whichis the data symbol for the co-scheduled UE, a is the power allocationvalue such that 0<α<1, and h is the n_(R)×1 channel vector (whichincludes precoding at the eNB, if any).

The log-likelihood ratio (LLR) for b_(0,1), the l-th bit of x₀ (where0<l<K₁), is the Log-MAP (LM) as shown in Equation (16) below:

$\begin{matrix}\begin{matrix}{{L\left( b_{0,l} \right)} = {\log \frac{P\left( {b_{0,l} = \left. 0 \middle| y \right.} \right)}{P\left( {b_{0,l} = \left. 1 \middle| y \right.} \right)}}} \\{= {\log \frac{{P\left( {\left. y \middle| b_{0,l} \right. = 0} \right)}{P\left( {b_{0,l} = 0} \right)}}{{P\left( {\left. y \middle| b_{0,l} \right. = 1} \right)}{P\left( {b_{0,l} = 1} \right)}}}} \\{= {\log \frac{\sum_{{x_{0}\text{:}b_{i,l}} = 0}{\sum_{x\; \prime_{0}}{P\left( {\left. y \middle| x_{0} \right.,x_{1}} \right)}}}{\sum_{{x_{0}\text{:}b_{i,l}} = 1}{\sum_{x\; \prime_{0}}{P\left( {\left. y \middle| x_{0} \right.,x_{1}} \right)}}}}} \\{= {\log \frac{\sum_{{x_{0}\text{:}b_{i,l}} = 0}{\sum_{x\; \prime_{0}}e^{- \frac{{{y - {h{({{\sqrt{\alpha}x_{0}} + {\sqrt{1 - \alpha}x\; \prime_{0}}})}}}}^{2}}{\sigma^{2}}}}}{\sum_{{x_{0}\text{:}b_{i,l}} = 1}{\sum_{x\; \prime_{0}}e^{- \frac{{{y - {h{({{\sqrt{\alpha}x_{0}} + {\sqrt{1 - \alpha}x\; \prime_{0}}})}}}}^{2}}{\sigma^{2}}}}}}}\end{matrix} & (16)\end{matrix}$

In the first approach, LLRs are obtained for the bits of the symbolx=√{square root over (α)}x₀+√{square root over (1−α)}x′₀ using the jointsoft-demapper as described below.

As an alternative approach, Max-Log-MAP approximation may be applied forone of the dimensions to get Equation (17) below:

$\begin{matrix}{{L\left( b_{0,l} \right)} = {\log \frac{\sum_{{x_{0}\text{:}b_{i,l}} = 0}{\max\limits_{x\; \prime_{0}}e^{- \frac{{{y - {h{({{\sqrt{\alpha}x_{0}} + {\sqrt{1 - \alpha}x\; \prime_{0}}})}}}}^{2}}{\sigma^{2}}}}}{\sum_{{x_{0}\text{:}b_{i,l}} = 1}{\max\limits_{x\; \prime_{0}}e^{- \frac{{{y - {h{({{\sqrt{\alpha}x_{0}} + {\sqrt{1 - \alpha}x\; \prime_{0}}})}}}}^{2}}{\sigma^{2}}}}}}} & (17)\end{matrix}$

This is identical to 2-layer transmission with effective (rank 1)channel matrix [√{square root over (α)}h, √{square root over (1−α)}h].Thus, an Rk 2 detector may be used for optimal or suboptimal symboldetection for 1-layer MUST transmission in the absence of a prioriinformation. If a priori information is available, the Rk2 LM approachcan be used.

To summarize, two approaches are possible for detection of scalar or1-layer superposition transmission:

-   -   Use joint soft-demapper to obtain LLRs for the bits of the        symbol x=√{square root over (α)}x₀+√{square root over (1−α)}x′₀.    -   Use rk2 LM with SIC or Turbo-DD if feasible approach assuming        effective (rank 1) channel matrix [√{square root over (α)}h,        √{square root over (1−α)}h].

Both the near UE and the far UE can adopt the above methods (the latteroption without SIC or Turbo-DD) if the modulation for the other user andthe power split information are both known.

In addition to the modulation order for the other user if MCS and radionetwork temporary identifier (RNTI) information for the other user areknown, it is possible for example for the near user to first obtain LLRfor the far user, decode the far user CW and perform SIC to cancel thefar user signal from the received signal. After this, the receiver cangenerate LLR for the near user symbols and perform decoding of the nearuser CW. In MUST context, this forms the CodeWord InterferenceCancellation (CWIC) method.

B. Multi-Layer Superposition

With respect to multi-layer superposition, the received signal can bewritten as Equation (18):

y=ν ₁(αx ₀ +βx′ ₀)+ν₂ x ₁ +n  (18)

Suppose that x₀ belongs to (2^(K) ¹ )-QAM constellation and x₁ belongsto (2^(K) ² )-QAM constellation, which are the two data symbols ofinterest, and x′₀ belongs to (2^(K) ³ )-QAM constellation which is thedata symbol for the co-scheduled UE.

The LLR for b_(0,1), the l-th bit of x₀ (where 0<l<K₁), is the Log-MAP(LM) as shown in Equation (19) below:

$\begin{matrix}\begin{matrix}{{L\left( b_{0,l} \right)} = {\log \frac{P\left( {b_{0,l} = \left. 0 \middle| y \right.} \right)}{P\left( {b_{0,l} = \left. 1 \middle| y \right.} \right)}}} \\{= {\log \frac{{P\left( {\left. y \middle| b_{0,l} \right. = 0} \right)}{P\left( {b_{0,l} = 0} \right)}}{{P\left( {\left. y \middle| b_{0,l} \right. = 1} \right)}{P\left( {b_{0,l} = 1} \right)}}}} \\{= {\log \frac{\sum_{{x_{0}\text{:}b_{i,l}} = 0}{\sum_{x_{1}}{\sum_{x\; \prime_{0}}{P\left( {\left. y \middle| x_{0} \right.,x_{1},x_{0}^{\prime}} \right)}}}}{\sum_{{x_{0}\text{:}b_{i,l}} = 1}{\sum_{x_{1}}{\sum_{x\; \prime_{0}}{P\left( {\left. y \middle| x_{0} \right.,x_{1},x_{0}^{\prime}} \right)}}}}}} \\{= {\log \frac{\sum_{{x_{0}\text{:}b_{i,l}} = 0}{\sum_{x_{1}}{\sum_{x\; \prime_{0}}e^{- \frac{{{y - {v_{1}{({{ax}_{0} + {\beta \; x\; \prime_{0}}})}} + {v_{2}x_{1}}}}^{2}}{\sigma^{2}}}}}}{\sum_{{x_{0}\text{:}b_{i,l}} = 1}{\sum_{x_{1}}{\sum_{x\; \prime_{0}}e^{- \frac{{{y - {v_{1}{({{ax}_{0} + {\beta \; x\; \prime_{0}}})}} + {v_{2}x_{1}}}}^{2}}{\sigma^{2}}}}}}}}\end{matrix} & (19)\end{matrix}$

In the first approach, rk2LM (with SIC or Turbo-DD if feasible) approachis used, as follows:

-   -   Treat [ν₁, ν₂] as the effective rank 2 channel;    -   obtain LLRs for the bits of symbol x₁ (which belongs to the        legacy M-QAM constellation);    -   obtain LLRs for the bits of the symbol x=αx₀+βx′₀, using the        joint soft-demapper.

For this case, the rk2 LM approach needs to be extended as shown below.

As an alternative, rk3/rk4 MIMO detector could be used by treating [αν₁,βν₁, ν₂x₁] as the effective channel matrix and assuming a 3-layertransmission. However, the rank of this effective channel is 2 since twoof the columns are linearly dependent. As a result, the rk3 MMSE step tofind the initial candidate x₀, etc., fails, at least at high SNR. On theother hand, rk3 lattice search methods can potentially be employed forobtaining LLRs of bits of x₀, x₁, and x′₀.

To summarize, two approaches are possible for detection of multi-layersuperposition transmission:

Use rk2 LM (with SIC or Turbo-DD if feasible) approach by obtaining LLRsfor the bits of the symbol x=αx₀+βx′₀ using the joint soft-demapper.

Use rk3 lattice search methods for obtaining LLRs of bits of x₀, x₁, andx′₀.

The above SLIC methods can be used by both the near UE and the far UE ifthe receiver knows the other user's modulation order and the power splitinformation.

The near UE can perform CWIC to cancel far user CW prior to decoding itsown CW if the MCS and RNTI information for the far user are known.

IV. LLR Generation for Receiving GNC Symbols

The constellation generated by the mapping above leads to a non-uniformconstellation since the constellation points are on an unequally spacedlattice. However, one property of the mapping is that the underlyingdirect-sum constellation is a (2^(K) ^(F) ^(+K) ^(N) )-QAMconstellation, albeit with non-uniform symbol boundaries. Therefore, theLLR computation logic may be extended for a Gray-encoded (2^(K) ^(F)^(+K) ^(N) )-QAM constellation by modifying the decision boundaries.

LLR generation for the m-th bit of the symbol in the non-uniform (2^(K)^(F) ^(+K) ^(N) )-QAM constellation is described. Since the LLR isgenerated jointly, whether this bit belongs to the near user or far user(i.e., desired user or co-scheduled user), can be ignored for the timebeing.

A. SISO/SIMO Soft Demapper Using Max-Log-MAP Approximation

With respect to SISO/SIMO soft demapper using MLM approximation, commonvariables y_(cb), CSI_(cb), I and Q can be defined as set forth below inEquations (20)(a) and (20)(b).

$\begin{matrix}{{y_{cb} = {\frac{h^{H}y}{\sqrt{C}} = {\frac{1}{\sqrt{C}}{\sum\limits_{j = 0}^{n_{R} - 1}{h_{j}^{*}y_{j}}}}}},{{CSI}_{cb} = {\frac{h}{\sqrt{C}}}^{2}}} & {(20)(a)} \\{{I = {{Re}\left( y_{cb} \right)}},{Q = {{Im}\left( y_{cb} \right)}}} & {(20)(b)}\end{matrix}$

The unnormalized symbol can be defined as set forth in Equation (21)below:

{dot over (x)}=√{square root over (C)}x  (21)

The LLR for bit m (ignoring whether this bit belongs to the near user orfar user) using max-log-MAP approximation can be defined as set forthbelow in Equation (22).

$\begin{matrix}{{L_{A}\left( b_{m} \right)} = {{- {\min\limits_{x \in X_{m}^{+}}\frac{{{y_{cb} - {{CSI}_{cb}\overset{.}{x}}}}^{2}}{{CSI}_{cb}\sigma_{n}^{2}}}} + {\min\limits_{x \in X_{M}^{-}}\frac{{{y_{cb} - {{CSI}_{cb}\overset{.}{x}}}}^{2}}{{CSI}_{cb}\sigma_{n}^{2}}}}} & (22)\end{matrix}$

As compared to the uniform constellation case, the constant C is nolonger fixed but rather is a function of the modulation pair andparameters p and q.

The symbol x∈S_(p,q)(X₁, X₂) belongs to a non-uniform constellationformed by the constellation pair (X₁, X₂).

For even values of m, LLR only depends on I, as shown in Equation(23)(a) below, and for odd values of m, LLR only depends on Q, as shownin Equation (23)(b) below:

$\begin{matrix}{\;^{\prime}{I = {\frac{1}{\sqrt{C}}\left( {{{h}^{2}x_{1}} + {{Re}\left( {h^{H}n} \right)}} \right)}}} & {(23)(a)} \\{\;^{\prime}{Q = {\frac{1}{\sqrt{C}}\left( {{{h}^{2}x_{Q}} + {{Im}\left( {h^{H}n} \right)}} \right)}}} & {(23)(b)}\end{matrix}$

By defining α=CSI_(cb) and

${{L_{A}\left( b_{m} \right)}^{\prime} = {\frac{\sigma_{n}^{2}}{4}{L_{A}\left( b_{m} \right)}}},$

Equation (22) can be rewritten as Equation (24):

$\begin{matrix}\begin{matrix}{{{L^{\prime}}_{A}\left( b_{m} \right)} = {\frac{\sigma_{n}^{2}}{4}\left( {{- {\min\limits_{x \in X_{m}^{+}}\frac{\left( {I - {a{\overset{.}{x}}_{I}}} \right)^{2}}{a\; \sigma_{n}^{2}}}} + {\min\limits_{x \in X_{m}^{-}}\frac{\left( {I - {a{\overset{.}{x}}_{I}}} \right)^{2}}{a\; \sigma_{n}^{2}}}} \right)}} \\{= {{- {\min\limits_{x \in X_{m}^{+}}\frac{\left( {I - {a{\overset{.}{x}}_{I}}} \right)^{2}}{4a}}} + {\min\limits_{x \in X_{m}^{-}}\frac{\left( {I - {a{\overset{.}{x}}_{I}}} \right)^{2}}{4a}}}}\end{matrix} & (24)\end{matrix}$

where x_(m) ⁺ denotes the subset of S_(p,q)(x₁,x₂), such that the m-thbit of each element in the subset is equal to ‘0’; and x_(m), denotesthe subset of S_(p,q)(X₁, X₂) such that the m-th bit of each element inthe subset is equal to ‘1’.

Using this framework, decision boundaries and LLR values can becalculated for SISO/SIMO soft demapping using MLM approximation. Thedecision boundaries for different bits correspond to a Gray-mappedsuper-constellation if power allocation satisfies the necessaryconditions for maintenance of Gray mapping. See, e.g., Tables 4 and 5above. For different modulation order pairs, Max-Log-MAP soft demapperexpressions can be derived under the assumption that Gray mapping ismaintained (with or without bit swapping).

Examples of specific equations, LLR values, and decision boundaries forGNC super-constellations in a rk1 SISO/SIMO transmission are provided inAPPENDIX II attached hereto, and in U.S. Prov. Pat. App. Ser. Nos.62/173,241 and 62/203,818, from which APPENDIX II is derived and thepresent application claims priority (and which have been incorporated byreference in their entirety).

In another embodiment of the present disclosure, it is shown that theLLR for bit b_(l) based on max-log-MAP approximation for the approachproposed earlier can be written down in the general form of Equations(25)(a) and (b):

L′ _(A)(b _(l))=g(p,q)Re(y _(cb))+h(p,q) for l even  (25)(a)

L′ _(A)(b _(l))=g(p,q)lm(y _(cb))+h(p,q) for l odd  (25)(b)

where g(p,q) and h(p,q) are two functions of parameters p, q, and:

$\begin{matrix}{{y_{cb} = {\frac{h^{H}y}{\sqrt{C}} = {\frac{1}{\sqrt{C}}{\sum\limits_{j = 0}^{n_{R} - 1}{h_{j}^{*}y_{j}}}}}}\;} & (26)\end{matrix}$

Equation (26) is determined based on the received signal vector and theestimated channel state.

B. SISO/SIMO Rank 1 Direct Soft Demapping Using Log-MAP

With respect to rank 1 Log-MAP for SISO/SIMO, a simplification is used;namely, that the number of Euclidean Distances (ED) required forcalculating LLR for all of the bits of GNC symbol is equal to 2^((K)^(F) ^(+K) ^(N) ^()/2+1) or 2√{square root over (M)}, where M=2^(K) ^(F)^(+K) ^(N) .

Assuming that simplification, the LLR for bit b_(m) in GNC can bewritten as Equation (27):

$\begin{matrix}\begin{matrix}{{L\left( b_{m} \right)} = {\log \frac{P\left( {b_{m} = {0y}} \right)}{P\left( {b_{m} = {1y}} \right)}}} \\{= {\log \frac{{P\left( {{yb_{m}} = 0} \right)}{P\left( {b_{m} = 0} \right)}}{{P\left( {{yb_{m}} = 1} \right)}{P\left( {b_{m} = 1} \right)}}}} \\{= {\log \frac{\sum\limits_{{x:b_{m}} = 0}^{\;}\; {P\left( {yx} \right)}}{\sum\limits_{{x:b_{m}} = 1}^{\;}\; {P\left( {yx} \right)}}}} \\{= {\log \frac{\sum\limits_{{x:b_{m}} = 0}^{\;}\; e^{- \frac{{{y - {hx}}}^{2}}{\sigma^{2}}}}{\sum\limits_{{x:b_{m}} = 1}^{\;}\; e^{- \frac{{{y - {hx}}}^{2}}{\sigma^{2}}}}}}\end{matrix} & (27)\end{matrix}$

where x∈S_(p,q)(X₁, X₂), X₁ is the first user's constellation, and X₂ issecond user's constellation.

Let S_(p,q) ^(I)(X₁, X₂) denote the real-valued set formed by projectionof the constellation symbols of S_(p,q)(X₁, X₂) on the I-axis andS_(p,q) ^(Q)(X₁, X₂) denote the real-valued set (ignoring the √{squareroot over (−1)} term) formed by projection of the constellation symbolsof S_(p,q) (X₁, X₂) on the Q-axis. Thus, for example, if X₁=X_(QPSK) andx₂=x_(16QAM), then:

$\begin{matrix}{{S_{p,q}^{I}\left( {\chi_{1},\chi_{2}} \right)} = {{S_{p,q}^{Q}\left( {\chi_{1},\chi_{2}} \right)} = \left\{ {{{{- 4}p} - {3{pq}}},{{{- 4}p} - {pq}},{{{- 4}p} + {pq}},{{{- 4}p} + {3{pq}}},{{4p} - {3{pq}}},{{4p} - {pq}},{{4p} + {pq}},{{4p} + {3{pq}}}} \right\}}} & (28)\end{matrix}$

Equation (29) below holds for SISO/SIMO:

$\begin{matrix}{\frac{{{y - {hx}}}^{2}}{\sigma^{2}} = {{\frac{1}{\sigma^{2}}\left\lbrack {{y}^{2} - {\frac{1}{h^{H}h}\left( {h^{H}y} \right)^{2}}} \right\rbrack} + {\frac{1}{\sigma^{2}h^{H}h}{{{h^{H}y} - {\left( {h^{H}h} \right)x}}}^{2}}}} & (29)\end{matrix}$

The first term on the right in the preceding equation

$\left( {\frac{1}{\sigma^{2}}\left\lbrack {{y}^{2} - {\frac{1}{h^{H}h}\left( {h^{H}y} \right)^{2}}} \right\rbrack} \right)$

does not depend on x. Using the symmetry of constellation points aroundthe I-axis for the set {x: b_(m)=0} and the set {x: b_(m)=1} for even m,then for even indexed m:

$\begin{matrix}{{\log \frac{\sum\limits_{{x:b_{m}} = 0}^{\;}\; e^{- \frac{{{y - {hx}}}^{2}}{\sigma^{2}}}}{\sum\limits_{{x:b_{m}} = 1}^{\;}\; e^{- \frac{{{y - {hx}}}^{2}}{\sigma^{2}}}}} = {\log \frac{\sum\limits_{{{z \in {S_{p \cdot q}^{I}{({\chi_{1},\chi_{2}})}}}:b_{m}} = 0}^{\;}e^{- \frac{{{{{Re}{\{{h^{H}y}\}}} - {{({h^{H}h})}z}}}^{2}}{\sigma^{2}}}}{\sum\limits_{{{z \in {S_{p \cdot q}^{I}{({\chi_{1},\chi_{2}})}}}:b_{m}} = 1}^{\;}e^{- \frac{{{{{Re}{\{{h^{H}y}\}}} - {{({h^{H}h})}z}}}^{2}}{\sigma^{2}}}}}} & (30)\end{matrix}$

The same simplification and calculation can be made for odd-indexed m.See Eq. (31)(b) below.

The set {x: b_(m)=0} has M/2 elements where M=2^(K) ^(F) ⁺ ^(K) ^(N).Therefore, when using the brute force approach, M Euclidean Distances(ED) would need to be computed to find the LLRs. However, the set{z∈S_(p.q) ^(I)(x₁, x₂): b_(m)=0} has only √{square root over (M)}elements. Accordingly, using the simplification above according to anembodiment of the present disclosure, only 2√{square root over (M)} EDswould need to be computed in order to calculate LLRs for all of the bitsof a GNC symbol.

To summarize, the LLRs for rk1 GNC transmission can be computed asEquations (31)(a) and (31)(b) below.

$\begin{matrix}{{{L\left( b_{m} \right)} = {\log \frac{\sum\limits_{{{z \in {S_{p \cdot q}^{I}{({\chi_{1},\chi_{2}})}}}:b_{m}} = 0}^{\;}e^{- \frac{{{{{Re}{\{{h^{H}y}\}}} - {{({h^{H}h})}z}}}^{2}}{\sigma^{2}}}}{\sum\limits_{{{z \in {S_{p \cdot q}^{I}{({\chi_{1},\chi_{2}})}}}:b_{m}} = 1}^{\;}e^{- \frac{{{{{Re}{\{{h^{H}y}\}}} - {{({h^{H}h})}z}}}^{2}}{\sigma^{2}}}}\mspace{14mu} {for}\mspace{14mu} {even}\mspace{14mu} m}}} & {(31)(a)} \\{\mspace{79mu} {{L\left( b_{m} \right)} = {\log \frac{\sum\limits_{{{z \in {S_{p \cdot q}^{Q}{({\chi_{1},\chi_{2}})}}}:b_{m}} = 0}^{\;}e^{- \frac{{{{{Im}{\{{h^{H}y}\}}} - {{({h^{H}h})}z}}}^{2}}{\sigma^{2}}}}{\sum\limits_{{{z \in {S_{p \cdot q}^{Q}{({\chi_{1},\chi_{2}})}}}:b_{m}} = 1}^{\;}e^{- \frac{{{{{Im}{\{{h^{H}y}\}}} - {{({h^{H}h})}z}}}^{2}}{\sigma^{2}}}}\mspace{14mu} {for}\mspace{14mu} {odd}\mspace{14mu} m}}} & {(31)(b)}\end{matrix}$

C. Rank 2 Log-MAP

The key step in rk2 Log-MAP without prior information is thatMax-Log-MAP (MLM) approximation is applied assuming layer 0 belongs tobe the soft layer and the hard slicing of x₁ is performed as in Equation(32) below:

$\begin{matrix}{{{\hat{x}}_{1}\left( x_{0} \right)} = {\underset{x_{1} \in {\mathbb{C}}_{1}}{\arg \mspace{11mu} \min}{{{h_{1}^{H}\left( {y - {h_{0}x_{0}}} \right)} - {h_{1}^{H}h_{1}x_{1}}}}^{2}}} & (32)\end{matrix}$

Three options are possible:

-   -   1. The cross-layer x₁ belongs to a non-uniform M-QAM        constellation S_(p,q)(X₁, X₂) and soft layer x₀ belongs to a        uniform M-QAM constellation.    -   2. The cross-layer x₁ belongs to a uniform M-QAM constellation        and soft layer x₀ belongs to a non-uniform M-QAM constellation        S_(p,q)(X₁, X₂).    -   3. Both soft layer and cross layer belong to non-uniform M-QAM        constellations S_(p,q)(X₁, X₂) and S_(p,q)(X₃, X₄),        respectively.

Compared to conventional slicers for uniform M-QAM constellations, thehard slicer proposed herein has modified decision boundaries to handlenon-uniform M-QAM constellations. This can be handled as a special caseof hard slicing with prior information.

rk2 Log-MAP iterative detection is possible if the UE is providedsufficient information (e.g., MCS, Cell RNTI (C-RNTI), and any otherpossibly pertinent information) to decode the co-scheduled UE's physicaldownlink shared channel (PDSCH) codeword. When iterative detection ispossible, iterative (turbo) soft interference cancellation is possible.

One of the key steps in rk2 Log-MAP without iterative detection is thatthe MLM approximation is applied assuming layer 0 to be the soft layerand the hard slicing of x₁ is performed as in Equation (33)(a) below:

$\begin{matrix}{{{\hat{x}}_{1}\left( x_{0} \right)} = {\underset{x_{1} \in {\mathbb{C}}_{1}}{\arg \mspace{11mu} \min}\left( {{{y - {Hx}}}^{2} - {\frac{\sigma^{2}}{2}{\sum\limits_{{({m,n})} \neq {({i,l})}}^{\;}\; {\left( {- 1} \right)^{b_{m,n}}{L_{a}\left( b_{m,n} \right)}}}}} \right)}} & {(33)(a)}\end{matrix}$

which is equivalent to Equation (33)(b) below:

$\begin{matrix}{{{\hat{x}}_{1}\left( x_{0} \right)} = {\underset{x_{1} \in {\mathbb{C}}_{1}}{\arg \mspace{11mu} \min}\left( {{{y - {Hx}}}^{2} - {\frac{\sigma^{2}}{2}{\sum\limits_{n}^{\;}\; {\left( {- 1} \right)^{b_{1,n}}{L_{a}\left( b_{1,n} \right)}}}}} \right)}} & {(33)(b)}\end{matrix}$

V. Control Signaling for GNC

The co-scheduled UEs according to embodiments of the present disclosureneed to be informed of one or more of:

-   -   1) the type of superposition transmission (e.g., no MUST,        1-layer MUST, or multi-layer MUST),    -   2) the modulation orders for the constituent users that are        co-scheduled, and    -   3) the power split factor α_(N)=1−α_(F) on the precoding vector        (or equivalently the demodulation reference signal (DMRS)        antenna port) applicable to near/far user PDSCH symbols.

Downlink Control Information (DCI) for Joint LLR or SLIC

As discussed above, in some embodiments, the BS/eNB dynamically (i)decides whether or not MUST is employed; (ii) selects a user pair (oruser triplet) and the corresponding MCS(s); and (iii) if MUST isemployed, determines the suitable α_(N)=1−α_(F) power split factor basedon the MCS selected. In such embodiments, the needed pieces ofinformation could be transmitted to the UEs as DCI over the physicaldownlink control channel (PDCCH)/enhanced physical downlink controlchannel (EPDCCH).

In MUST schemes, the range of values of α_(N)=1−α_(F) that is ofinterest is determined based on p,q values. Under the GNC definition,p=1 is always true since it is scaled out by the normalization factor asdescribed above. Thus, the eNB only needs to signal one of (1) α_(N),(2) α_(F), and (3) q values. Once the modulation orders and the userranks are indicated, and one of (1) α_(N), (2) α_(F), and (3) q valuesare provided, the receiving UE will be able to deduce the otherparameters.

When provided to the UE via control signaling, α_(N) or α_(F) can beselected from a small set of feasible values. For example, if systemsimulations determine that the relevant range for α_(F) is α_(F)∈[0.2,1), this range set can be reduced to a finite alphabet set, suchas, for example, {0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9} which includes thedifferent ratios necessary to obtain the non-uniform S_(p,q)(X₁, X₂)constellations of interest. Similarly, the q value, when provided to theUE via control signaling, can be transmitted in DCI once again based ona finite alphabet.

As discussed above, when α_(F) enters a certain range, Gray mapping isviolated and the BS/eNB scheduler may decide to use Direct SymbolMapping (DSM) rather than GNC mapping. In such a scenario, the BS/eNBcan send an indication in DCI to indicate whether it is using, in agiven TTI, (1) GNC mapping without bit swapping; (2) GNC mapping withbit swapping; or (3) DSM. The UE can use this information toappropriately configure its detecting, decoding, and processing, basedon the type of mapping used.

In LTE Rel-12, DCI Format 2C has a three-bit field indicating “antennaport(s), scrambling identity and number of layers”. See, e.g., 3GPP TS36.212, v. 12.0.0 (2013-12), which is hereby incorporated by referencein its entirety, § 5.3.3.1.5C. In addition, 3GPP TS 36.211 v. 12.5.0(2015-03) is hereby incorporated by reference in its entirety. Thisthree-bit field, which can thus take the values 0-7, indicates themessages as shown in Table 5 below, which is based on Table 5.3.3.1.5C-1in TS 36.212:

TABLE 5 DCI Format 2C “Antenna port(s), . . . ” Field Values OneCodeword: Two Codewords: Codeword 0 enabled, Codeword 0 enabled,Codeword 1 disabled Codeword 1 enabled value Message value Message 0 1layer, port 7, n_(SCID) = 0 0 2 layers, ports 7-8, n_(SCID) = 0 1 1layer, port 7, n_(SCID) = 1 1 2 layers, ports 7-8, n_(SCID) = 1 2 1layer, port 8, n_(SCID) = 0 2 3 layers, ports 7-9 3 1 layer, port 8,n_(SCID) = 1 3 4 layers, ports 7-10 4 2 layers, ports 7-8 4 5 layers,ports 7-11 5 3 layers, ports 7-9 5 6 layers, ports 7-12 6 4 layers,ports 7-10 6 7 layers, ports 7-13 7 Reserved 7 8 layers, ports 7-14

Since MCS is independently controllable on ports 7 and 8 during 2 layertransmission and on ports 7/8 and 9/10 during 4 layer transmission, whenMUST is employed (i.e., with two users), the possibilities are that:

-   -   1) in 1 layer transmission, the other user is co-scheduled on        port 7;    -   2) in 2 layer transmission, the other user is co-scheduled on        port 7 or port 7/8;    -   3) in 3 layer transmission, the other user is co-scheduled on        port 7 or port 7/8 or port 7/8/9; and    -   4) in 4 layer transmission, the other user is co-scheduled on        port 7 or port 7/8 or port 7/8/9 or port 7/8/9/10.

Accordingly, the three-bit field indicating “antenna port(s), . . . ” inDCI Format 2C already contains the information to convey theco-scheduled user transmission state and the number of transmissionlayers. One of the signaling states, such as, for example, the RESERVEDmessage for field value=7 (for one codeword) can be used to indicatewhether there is a MUST transmission.

The above-described signaling is more general than what is needed forMUST Scenario 1 and MUST Scenario 2. In Table 5, nSCID allocation by theeNb is fully flexible for the user and the co-scheduled user.

At least the modulation order(s) for the co-scheduled user's one or morelayers also needs to be signaled by the eNb or blindly estimated by theUE. For example, up to two MCSs (which determine the modulation ordersfor up to 4 layers) can be indicated, but this is unnecessary for SLIC,which does not need to know the coding rates so the modulation order isenough. Instead, the two modulation orders (for up to 4 layers) can bedirectly signaled. Since there are 4 modulation orders in LTE Rel-12{QPSK, 16QAM, 64QAM, 256QAM}, only 2 bits are needed to indicate themodulation order if it is signaled by the eNb. Accordingly, assumingK=2, a maximum of 2*2=4 bits are needed to indicate the co-scheduleduser modulation on all of its layers. More generally, *2 bits are neededfor each UE.

In summary, in one embodiment of the present disclosure, the MUSTcontrol information which needs to be blindly estimated by the UE orsignaled by, for example, DCI, should include:

-   -   1) a MUST or no MUST indication;    -   2) one of (i) α_(N), (ii) α_(F), and (iii) q values;    -   3) 1-bit indication whether GNC mapping or DSM is used in a TTI;    -   4) co-scheduled user's antenna port(s), scrambling identity, and        number of layers indication; and    -   5) co-scheduled user's modulation order (pair) for SLIC or MCS        (pair) indication for CWIC.

Downlink Control Information (DCI) for CWIC

If the near UE needs to be able to perform CWIC, the co-scheduled UEMCS/TB information needs to be signaled in DCI in addition to theinformation elements described above.

In TS 36.212, for co-scheduled user transport block 1:

-   -   Modulation and coding scheme—5 bits    -   New data indicator—1 bit    -   Redundancy version—2 bits

In TS 36.212, for co-scheduled user transport block 2:

-   -   Modulation and coding scheme—5 bits    -   New data indicator—1 bit    -   Redundancy version—2 bits

The signal RNTI information (such as, for example, C-RNTI, andSemi-persistent C-RNTI (SPS-C-RNTI)) for the co-scheduled user can besignaled in DCI. However, this will likely lead to a large overhead.Instead the RNTI information and the associated co-scheduler user indexcan be indicated via radio resource control (RRC). The DCI can include aco-scheduled user index pointer, which points to the RNTI informationsent ahead of time in RRC signaling.

Depending on the embodiment of the present disclosure, steps and/oroperations in accordance with the present disclosure may occur in adifferent order, or in parallel, or concurrently for different epochs,or a combination of the same, in different embodiments, as would beunderstood by one of ordinary skill in the art. Similarly, as would beunderstood by one of ordinary skill in the art, FIGS. 4, 5, and 6 aresimplified representations of the actions performed, and real-worldimplementations may perform the actions in a different order or bydifferent ways or means. Similarly, as simplified representations, FIGS.4, 5, and 6 do not show other required steps as these are known andunderstood by one of ordinary skill in the art and not pertinent and/orhelpful to the present description.

Depending on the embodiment of the present disclosure, some or all ofthe steps and/or operations may be implemented or otherwise performed,at least in part, on a portable device. “Portable device” as used hereinrefers to any portable, mobile, or movable electronic device having thecapability of receiving wireless signals, including, but not limited to,multimedia players, communication devices, computing devices, navigatingdevices, etc. Thus, mobile devices include, but are not limited to,laptops, tablet computers, Portable Digital Assistants (PDAs), mp3players, handheld PCs, Instant Messaging Devices (IMD), cellulartelephones, Global Navigational Satellite System (GNSS) receivers,watches, cameras or any such device which can be worn and/or carried onone's person. “User Equipment” or “UE” as used herein corresponds to theusage of that term in the 3GPP LTE/LTE-A protocols, but is not in anyway limited by the 3GPP LTE/LTE-A protocols. Moreover, “User Equipment”or “UE” refers to any type of device, including portable devices, whichacts as a wireless receiver.

Depending on the embodiment of the present disclosure, some or all ofthe steps and/or operations may be implemented or otherwise performed,at least in part, using one or more processors running instruction(s),program(s), interactive data structure(s), client and/or servercomponents, where such instruction(s), program(s), interactive datastructure(s), client and/or server components are stored in one or morenon-transitory computer-readable media. The one or more non-transitorycomputer-readable media may be instantiated in software, firmware,hardware, and/or any combination thereof. Moreover, the functionality ofany “module” discussed herein may be implemented in software, firmware,hardware, and/or any combination thereof.

The one or more non-transitory computer-readable media and/or means forimplementing/performing one or more operations/steps/modules ofembodiments of the present disclosure may include, without limitation,application-specific integrated circuits (“ASICs”), standard integratedcircuits, controllers executing appropriate instructions (includingmicrocontrollers and/or embedded controllers), field-programmable gatearrays (“FPGAs”), complex programmable logic devices (“CPLDs”), and thelike. Some or all of any system components and/or data structures mayalso be stored as contents (e.g., as executable or other non-transitorymachine-readable software instructions or structured data) on anon-transitory computer-readable medium (e.g., as a hard disk; a memory;a computer network or cellular wireless network or other datatransmission medium; or a portable media article to be read by anappropriate drive or via an appropriate connection, such as a DVD orflash memory device) so as to enable or configure the computer-readablemedium and/or one or more associated computing systems or devices toexecute or otherwise use or provide the contents to perform at leastsome of the described techniques. Some or all of any system componentsand data structures may also be stored as data signals on a variety ofnon-transitory computer-readable transmission mediums, from which theyare read and then transmitted, including across wireless-based andwired/cable-based mediums, and may take a variety of forms (e.g., aspart of a single or multiplexed analog signal, or as multiple discretedigital packets or frames). Such computer program products may also takeother forms in other embodiments. Accordingly, embodiments of thisdisclosure may be practiced in any computer system configuration.

Thus, the term “non-transitory computer-readable medium” as used hereinrefers to any medium that comprises the actual performance of anoperation (such as hardware circuits), that comprises programs and/orhigher-level instructions to be provided to one or more processors forperformance/implementation (such as instructions stored in anon-transitory memory), and/or that comprises machine-level instructionsstored in, e.g., firmware or non-volatile memory. Non-transitorycomputer-readable media may take many forms, such as non-volatile andvolatile media, including but not limited to, a floppy disk, flexibledisk, hard disk, RAM, PROM, EPROM, FLASH-EPROM, EEPROM, any memory chipor cartridge, any magnetic tape, or any other magnetic medium from whicha computer instruction can be read; a CD-ROM, DVD, or any other opticalmedium from which a computer instruction can be read, or any othernon-transitory medium from which a computer instruction can be read.

While the invention has been shown and described with reference tocertain embodiments thereof, it will be understood by those skilled inthe art that various changes in form and detail may be made thereinwithout departing from the spirit and scope of the invention as definedby the appended claims.

Appendix I

TABLE AI-1 (QPSK, QPSK) (QPSK, QPSK) = 16-QAM Super-constellation =S_(p,q) (X_(QPSK), X_(QPSK)) Bit Mapping (b₀, b₁) = (d₀ ^(F)d₁ ^(F))(b₂, b₃) = (d₀ ^(N)d₁ ^(N))$\quad{x = {\frac{1}{\sqrt{C}}\left\{ {{{p\left( {1 - {2b_{0}}} \right)}\left\lbrack {2 - {q\left( {1 - {2b_{2}}} \right)}} \right\rbrack} + {{{jp}\left( {1 - {2b_{1}}} \right)}\left\lbrack {2 - {q\left( {1 - {2b_{3}}} \right)}} \right\rbrack}} \right\}}}$Symbol Mapping$\quad{x = {\frac{1}{\sqrt{C}}\left\{ {{p\; {\left( {1 - {2d_{0}^{F}}} \right)\left\lbrack {2 - {q\; \left( {1 - {2d_{0}^{N}}} \right)}} \right\rbrack}} + {{jp}\; {\left( {1 - {2d_{1}^{F}}} \right)\left\lbrack {2 - {q\; \left( {1 - {2d_{1}^{N}}} \right)}} \right\rbrack}}} \right\}}}\;$→Setting p = q = 1 or equivalently α_(F) > 0.8 results in thetraditional 16QAM constellation Constraints for Scenario 1(scalar/1-layer): Constraints for Scenario 2 (two-layer): 1) 2p²(4 + q²)= C which arises from unit 1) 2p²(4 + q²) = 0.5C(1 + α_(F)) andconstellation power and${\left. 2 \right)\mspace{14mu} \frac{q^{2}}{4}} = {\frac{1 - \alpha_{F}}{2\alpha_{F}}.}$${{\left. 2 \right)\mspace{14mu} \frac{q^{2}}{4}} = \frac{1 - \alpha_{F}}{\alpha_{F}}},{{which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}}$power split requirement between (b₀, b₁) bits and (b₂, b₃) bits.

Appendix I

TABLE AI-2 (16-QAM, QPSK) (16-QAM, QPSK) = 64-QAM Super-Constellation =S_(p,q) (X_(16QAM), X_(QPSK)) Bit Mapping (b₀, b₁, b₂, b₃) = (d₀ ^(F)d₁^(F)d₂ ^(F)d₃ ^(F)) (b₄, b₅) = (d₀ ^(N) d₁ ^(N)) Symbol Mapping$\quad\begin{matrix}{x = {\frac{1}{\sqrt{C}}\left\{ {{\left( {1 - {2d_{0}^{F}}} \right){p\mspace{11mu}\left\lbrack {4 - {\left( {1 - {2d_{2}^{F}}} \right)\left\lbrack {2 - {q\left( {1 - {2d_{0}^{N}}} \right)}} \right\rbrack}} \right\rbrack}} +} \right.}} \\\left. {j\; \left( {1 - {2d_{1}^{F}}} \right){p\left\lbrack {4 - {\left( {1 - {2d_{3}^{F}}} \right)\left\lbrack {2 - {q\; \left( {1 - {2d_{1}^{N}}} \right)}} \right\rbrack}} \right\rbrack}} \right\}\end{matrix}$ → Setting p = q = 1 or equivalently α_(F) = 20/21 resultsin the traditional 64QAM constellation. Constraints for Scenario 1(scalar/1-layer): Constraints for Scenario 2 (two-layer): 1) 2p²(20 +q²) = C which arises from unit 1) 2p²(20 + q²) = 0.5C(1 + αF), andconstellation power, and${\left. 2 \right)\mspace{14mu} \frac{q^{2}}{20}} = {\frac{1 - \alpha_{F}}{2\; \alpha_{F}}.}$${{\left. 2 \right)\mspace{14mu} \frac{q^{2}}{20}} = \frac{1 - \alpha_{F}}{\alpha_{F}}},{{which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$split requirement between (b₀, b₁, b₂, b₃) bits and (b₄, b₅) bits.

Appendix I

TABLE AI-3 (QPSK,16-QAM) (QPSK, 16-QAM) = 64-QAM Super-Constellation =S_(p,q)(X_(QPSK), X_(16QAM)) Bit Mapping (b₀, b₁) = (d₀ ^(F), d₁ ^(F))(b₂,b₃,b₄,b₅) = (d₀ ^(N), d₁ ^(N), d₂ ^(N), d₃ ^(N)) Symbol Mapping$\quad\begin{matrix}{x = {\frac{1}{\sqrt{C}}\left\{ {{\left( {1 - {2d_{0}^{F}}} \right){p\mspace{11mu}\left\lbrack {4 - {q\; {\left( {1 - {2d_{0}^{N}}} \right)\left\lbrack {2 - \left( {1 - {2d_{2}^{N}}} \right)} \right\rbrack}}} \right\rbrack}} +} \right.}} \\\left. {{j\left( {1 - {2d_{1}^{F}}} \right)}{p\left\lbrack {4 - {{q\left( {1 - {2d_{1}^{N}}} \right)}\left\lbrack {2 - \left( {1 - {2d_{3}^{N}}} \right)} \right\rbrack}} \right\rbrack}} \right\}\end{matrix}$ →Setting p = q = 1 or equivalently α_(F) = 16/21 resultsin the traditional 64QAM constellation. For Scenario 1 (scalar/l-layer):For Scenario 2 (two-layer): 1) 2p²(16 + 5q²) = C which arises from 1)2p²(16 + 5q²) =0.5C(1 + α_(F)) which arises unit constellation power,and from unit constellation power, and${\left. 2 \right)\mspace{14mu} \frac{10q^{2}}{32}} = {\frac{1 - \alpha_{F}}{\alpha_{F}}\mspace{14mu} {which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$${\left. 2 \right)\mspace{14mu} \frac{10q^{2}}{32}} = {\frac{1 - \alpha_{F}}{2\alpha_{F}}\mspace{14mu} {which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$split requirement between (b₀, b₁) bits and split requirement between(b0, b1) bits and (b₂, b₃, b₄, b₅) bits. (b2, b3, b4, b5) bits.

Appendix I

TABLE AI-4 (16-QAM,16-QAM) (16-QAM, 16-QAM) = 256-QAMSuper-Constellation = S_(p,q)(X_(16QAM), X_(16QAM)) Bit Mapping (b₀, b₁,b₂, b₃) = (d₀ ^(F), d₁ ^(F), d₂ ^(F), d₃ ^(F)) (b₄, b₅, b₆, b₇) = (d₀^(N), d₁ ^(N), d₂ ^(N), d₃ ^(N)) Symbol Mapping $\quad\begin{matrix}{x = {\frac{1}{\sqrt{C}}\left\{ {{p\; {\left( {1 - {2d_{0}^{F}}} \right)\left\lbrack {8 - {\left( {1 - {2d_{2}^{F}}} \right)\left\lbrack {4 - {q\; {\left( {1 - {2d_{0}^{N}}} \right)\left\lbrack {2 - \left( {1 - {2d_{2}^{N}}} \right)} \right\rbrack}}} \right\rbrack}} \right\rbrack}} +} \right.}} \\\left. {{{jp}\left( {1 - {2d_{1}^{F}}} \right)}\left\lbrack {8 - {\left( {1 - {2d_{3}^{F}}} \right)\left\lbrack {4 - {q{\left( {1 - {2d_{1}^{N}}} \right)\left\lbrack {2 - \left( {1 - {2d_{3}^{N}}} \right)} \right\rbrack}}} \right\rbrack}} \right\rbrack} \right\}\end{matrix}$ →Setting p = q = 1 or equivalently α_(F) = 16/17 resultsin the traditional 256QAM constellation. For Scenario 1:(scalar/1-layer) For Scenario 2 (two-layer): 1) 2p²(80 + 5q²) = C whicharises from unit 1) 2p²(80 + 5q²) = 0.5C(l + α_(F)) which arisesconstellation power and from unit constellation power and${\left. 2 \right)\mspace{14mu} \frac{q^{2}}{16}} = {\frac{1 - \alpha_{F}}{\alpha_{F}}{which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$${\left. 2 \right)\mspace{14mu} \frac{q^{2}}{16}} = {\frac{1 - \alpha_{F}}{2\alpha_{F}}{which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$split requirement between (b₀, b₁, b₂, b₃) bits split requirementbetween (b₀, b₁, b₂, b₃) bits and (b₄, b₅, b₄, b₅) bits. and (b₄, b₅,b₄, b₅) bits.

Appendix I

TABLE AI5 (64-QAM, QPSK) (64-QAM, QPSK) = 256-QAM Super-Constellation =S_(p,q)(X_(64QAM), X_(QPSK)) Bit Mapping (b₀, b₁, b₂, b₃, b₄, b₅) = (d₀^(F), d₁ ^(F), d₂ ^(F), d₃ ^(F), d₄ ^(F), d₅ ^(F)) (b₆, b₇) = (d₀ ^(N),d₁ ^(N)) Symbol Mapping $\quad\begin{matrix}{x = {\frac{1}{\sqrt{C}}\left\{ {{p\; {\left( {1 - {2d_{0}^{F}}} \right)\left\lbrack {8 - {\left( {1 - {2d_{2}^{F}}} \right)\left\lbrack {4 - {\left( {1 - {2d_{4}^{F}}} \right)\left\lbrack {2 - {q\; \left( {1 - {2d_{0}^{N}}} \right)}} \right\rbrack}} \right\rbrack}} \right\rbrack}} +} \right.}} \\\left. {{jp}\; {\left( {1 - {2d_{1}^{F}}} \right)\left\lbrack {8 - {\left( {1 - {2d_{3}^{F}}} \right)\left\lbrack {4 - {\left( {1 - {2d_{5}^{F}}} \right)\left\lbrack {2 - {q\; \left( {1 - {2d_{1}^{N}}} \right)}} \right\rbrack}} \right\rbrack}} \right\rbrack}} \right\}\end{matrix}$ →Setting p = q = 1 or equivalently α_(F) = 84/85 resultsin the traditional 256QAM constellation. For Scenario 1(scalar/1-layer): For Scenario 2 (two-layer): 1) 2p²(84 + q²) = C whicharises from unit 1) 2p²(84 + q²) = 0.5C(l + α_(F)) which arisesconstellation power and from unit constellation power, and${\left. 2 \right)\mspace{14mu} \frac{q^{2}}{84}} = {\frac{1 - \alpha_{F}}{\alpha_{F}}{which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$${\left. 2 \right)\mspace{14mu} \frac{q^{2}}{84}} = {\frac{1 - \alpha_{F}}{2\alpha_{F}}{which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$split requirement between split requirement between (b₀, b₁, b₂, b₃, b₄,b₅) bits and (b₆, b₇) bits. (b₀, b₁, b₂, b₃, b₄, b₅) bits and (b₆, b₇)bits.

Appendix I

TABLE AI-6 (QPSK, 64-QAM) (QPSK, 64-QAM) = 256-QAM Super-Constellation =S_(p,q)(X_(QPSK), X_(64QAM)) Bit Mapping (b₀, b₁) = (d₀ ^(F), d₁ ^(F))(b₂, b₃, b₄, b₅, b₆, b₇) = (d₀ ^(N), d₁ ^(N), d₂ ^(N), d₃ ^(N), d₄ ^(N),d₅ ^(N)) Symbol Mapping $\quad\begin{matrix}{x = {\frac{1}{\sqrt{C}}\left\{ {{p\; {\left( {1 - {2d_{0}^{F}}} \right)\left\lbrack {8 - {q\; {\left( {1 - {2d_{0}^{N}}} \right)\left\lbrack {4 - {\left( {1 - {2d_{2}^{N}}} \right)\left\lbrack {2 - \left( {1 - {2d_{4}^{N}}} \right)} \right\rbrack}} \right\rbrack}}} \right\rbrack}} +} \right.}} \\\left. {{jp}\; {\left( {1 - {2d_{1}^{F}}} \right)\left\lbrack {8 - {q\; {\left( {1 - {2d_{1}^{N}}} \right)\left\lbrack {4 - {\left( {1 - {2d_{3}^{N}}} \right)\left\lbrack {2 - \left( {1 - {2d_{5}^{N}}} \right)} \right\rbrack}} \right\rbrack}}} \right\rbrack}} \right\}\end{matrix}$ →Setting p = q = 1 or equivalently α_(F) = 64/85 resultsin the traditional 256QAM constellation. For Scenario 1(scalar/l-layer): For Scenario 2 (two-layer): 1) 2p²(64 + 21q²) = Cwhich arises from unit 1) 2p²(64 + 21q²) = 0.5C(1 + α_(F)) which arisesconstellation power and from unit constellation power and${\left. 2 \right)\mspace{14mu} \frac{21q^{2}}{64}} = {\frac{1 - \alpha_{F}}{\alpha_{F}}{which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$${\left. 2 \right)\mspace{14mu} \frac{21q^{2}}{64}} = {\frac{1 - \alpha_{F}}{2\alpha_{F}}\mspace{14mu} {which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$split requirement between split requirement between (b₀, b₁, b₂, b₃, b₄,b₅) bits and (b₆, b₇) bits. (b₀, b₁, b₂, b₃, b₄, b₅) bits and (b₆, b₇)bits.

Appendix I

TABLE AI-7 (64-QAM, 16-QAM) (64-QAM, 16-QAM) = 1024-QAMSuper-Constellation = S_(p,q)(X_(64QAM), X_(16QAM)) Bit Mapping (b₀, b₁,b₂, b₃, b₄, b₅) = (d₀ ^(F), d₁ ^(F), d₂ ^(F), d₃ ^(F), d₄ ^(F), d₅ ^(F))(b₆, b₇, b₈, b₉) = (d₀ ^(N), d₁ ^(N), d₂ ^(N), d₃ ^(N))$\quad\begin{matrix}{x = {\frac{1}{\sqrt{682}}\left\{ {{\left\{ {1 - {2b_{0}}} \right)\left\lbrack {16 - {\left( {1 - {2b_{2}}} \right)\left\lbrack {8 - {\left\lbrack {1 - {2b_{4}}} \right)\left\lbrack {4 - {\left( {1 - {2b_{6}}} \right)\left\lbrack {2 - \left( {1 - {2b_{8}}} \right)} \right\rbrack}} \right\rbrack}} \right\rbrack}} \right\rbrack} +} \right.}} \\\left. {{j\left( {1 - {2b_{1}}} \right)}\left\lbrack {16 - {\left( {1 - {2b_{3}}} \right)\left\lbrack {8 - {\left( {1 - {2b_{5}}} \right)\left\lbrack {4 - {\left( {1 - {2b_{7}}} \right)\left\lbrack {2 - \left( {1 - {2b_{9}}} \right)} \right\rbrack}} \right\rbrack}} \right\rbrack}} \right\rbrack} \right\}\end{matrix}$ Symbol Mapping $\quad\begin{matrix}{x = {\frac{1}{\sqrt{C}}\left\{ {{p\; {\left( {1 - {2d_{0}^{F}}} \right)\left\lbrack {16 - {\left( {1 - {2d_{2}^{F}}} \right)\left\lbrack {8 - {\left( {1 - {2d_{4}^{F}}} \right)\left\lbrack {4 - {q{\left( {1 - {2d_{0}^{N}}} \right)\left\lbrack {2 - \left( {1 - {2d_{2}^{N}}} \right)} \right\rbrack}}} \right\rbrack}} \right\rbrack}} \right\rbrack}} +} \right.}} \\\left. {{{jp}\left( {1 - {2d_{1}^{F}}} \right)}\left\lbrack {16 - {\left( {1 - {2d_{3}^{F}}} \right)\left\lbrack {8 - {\left( {1 - {2d_{5}^{F}}} \right)\left\lbrack {4 - {q\; {\left( {1 - {2d_{1}^{N}}} \right)\left\lbrack {2 - \left( {1 - {2d_{3}^{N}}} \right)} \right\rbrack}}} \right\rbrack}} \right\rbrack}} \right\rbrack} \right\}\end{matrix}$ →Setting p = q = 1 or equivalently α_(F) = 5/341 resultsin the traditional 1024QAM constellation. For Scenario 1(scalar/1-layer): For Scenario 2 (two-layer): 1) 2p² (336 + 5q²) = Cwhich arises from 1) 2p²(336 + 5q²) = 0.5C(1 + α_(F)), which arises unitconstellation power and from unit constellation power, and${\left. 2 \right)\mspace{14mu} \frac{5q^{2}}{336}} = {\frac{1 - \alpha_{F}}{\alpha_{F}}\mspace{14mu} {which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$${\left. 2 \right)\mspace{14mu} \frac{5q^{2}}{336}} = {\frac{1 - \alpha_{F}}{\alpha_{F}}\mspace{14mu} {which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$power split requirement between power split requirement between (b₀, b₁,b₂, b₃, b₄, b₅) bits and (b₆, b₇, b₈, b₉) (b₀, b₁, b₂, b₃, b₄, b₅) bitsand (b₆, b₇, b₈, b₉) bits. bits.

Appendix I

TABLE AI-8 (16-QAM, 64-QAM) (16-QAM, 64-QAM) = 1024-QAMSuper-Constellation = S_(p,q)(X_(16QAM), X_(64QAM)) Bit Mapping (b₀, b₁,b₂, b₃) = (d₀ ^(F), d₁ ^(F), d₂ ^(F), d₃ ^(F)) (b₄, b₅, b₆, b₇, b₈, b₉,)= (d₀ ^(N), d₁ ^(N), d₂ ^(N), d₃ ^(N), d₄ ^(N), d₅ ^(N)) Symbol Mapping$\quad\begin{matrix}{x = {\frac{1}{\sqrt{C}}\left\{ {{p\left( {1 - {2d_{0}^{F}}} \right)}\left\lbrack {16 - {\left( {1 - {2d_{2}^{F}}} \right)\left\lbrack {8 - {q\; {\left( {1 - {2d_{0}^{N}}} \right)\left\lbrack {4 -} \right.}}} \right.}} \right.} \right.}} \\{\left. \left. \left. {\left( {1 - {2d_{2}^{N}}} \right)\left\lbrack {2 - \left( {1 - {2d_{4}^{N}}} \right)} \right\rbrack} \right\rbrack \right\rbrack \right\rbrack + {{jp}\; {\left( {1 - {2d_{1}^{F}}} \right)\left\lbrack {16 - {\left( {1 - {2d_{3}^{F}}} \right)\left\lbrack {8 -} \right.}} \right.}}} \\\left. \left. \left. {{q\left( {1 - {2d_{1}^{N}}} \right)}\left\lbrack {4 - {\left( {1 - {2d_{3}^{N}}} \right)\left\lbrack {2 - \left( {1 - {2d_{5}^{N}}} \right)} \right\rbrack}} \right\rbrack} \right\rbrack \right\rbrack \right\}\end{matrix}$ →Setting p = q = 1 or equivalently α_(F) = 21/341 resultsin the traditional 1024QAM constellation. For Scenario 1(scalar/1-layer): For Scenario 2 (two-layer): 1) 2p²(320 + 21q²) = C,which arises from 1) 2p²(320 + 21q²) = 0.5C(1 + αF), which unitconstellation power, and arises from unit constellation power, and${{\left. 2 \right)\mspace{14mu} \frac{21q^{2}}{320}} = \frac{1 - \alpha_{F}}{\alpha_{F}}},{{which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$${{\left. 2 \right)\mspace{14mu} \frac{21q^{2}}{320}} = \frac{1 - \alpha_{F}}{\alpha_{F}}},{{which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$split requirement between split requirement between (b₀, b₁, b₂, b₃)bits and (b₄, b₅, b₆, b₇, b₈, b₉) (b₀, b₁, b₂, b₃) bits and bits. (b₄,b₅, b₆, b₇, b₈, b₉) bits.

Appendix I

TABLE AI-9 (64-QAM, 64-QAM) (64-QAM, 64-QAM) = 4096-QAMSuper-Constellation = Bit Mapping (b₀, b₁, b₂, b₃, b₄, b₅) = (d₀ ^(F),d₁ ^(F), d₂ ^(F), d₃ ^(F), d₄ ^(F), d₅ ^(F)) (b₆, b₇, b₈, b₉, b₁₀, b₁₁ )= (d₀ ^(N), d₁ ^(N), d₂ ^(N), d₃ ^(N), d₄ ^(N), d₅ ^(N))$\quad\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{x = {\frac{1}{\sqrt{2730}}\left\{ {\left( {1 - {2b_{0}}} \right)\left\lbrack {32 -} \right.} \right.}} \\{\left( {1 - {2b_{2}}} \right)\left\lbrack {16 - {\left( {1 - {2b_{4}}} \right)\left\lbrack {8 - {\left( {1 - {2b_{6}}} \right)\left\lbrack {4 -} \right.}} \right.}} \right.}\end{matrix} \\{\left. \left. \left. \left. {\left( {1 - {2b_{8}}} \right)\left\lbrack {2 - \left( {1 - {2b_{10}}} \right)} \right\rbrack} \right\rbrack \right\rbrack \right\rbrack \right\rbrack + {{j\left( {1 - {2b_{1}}} \right)}\left\lbrack {32 -} \right.}}\end{matrix} \\{\left( {1 - {2b_{3}}} \right)\left\lbrack {16 - {\left( {1 - {2b_{5}}} \right)\left\lbrack {8 -} \right.}} \right.}\end{matrix} \\\left. \left. \left. \left. {\left( {1 - {2b_{7}}} \right)\left\lbrack {4 - {\left( {1 - {2b_{9}}} \right)\left\lbrack {2 - \left( {1 - {2b_{11}}} \right)} \right\rbrack}} \right\rbrack} \right\rbrack \right\rbrack \right\rbrack \right\}\end{matrix}$ Symbol Mapping $\quad\begin{matrix}{x = {{\frac{1}{\sqrt{C}}\left\{ {p\left( {1 - {2d_{0}^{F}}} \right)} \right\rbrack 32} -}} \\{\left( {1 - {2d_{2}^{F}}} \right)\left\lbrack {16 - {\left( {1 - {2d_{4}^{F}}} \right)\left\lbrack {8 -} \right.}} \right.} \\{{q\left( {1 - {2d_{0}^{N}}} \right)}\left\lbrack {4 - {\left( {1 - {2d_{2}^{N}}} \right)\left\lbrack {2 -} \right.}} \right.} \\{\left. \left. \left. \left. \left. \left( {1 - {2d_{4}^{N}}} \right) \right\rbrack \right\rbrack \right\rbrack \right\rbrack \right\rbrack + {{{jp}\left( {1 - {2d_{1}^{F}}} \right)}\left\lbrack {32 -} \right.}} \\{\left( {1 - {2d_{3}^{F}}} \right)\left\lbrack {16 - {\left( {1 - {2d_{5}^{F}}} \right)\left\lbrack {8 - {q\left( {1 -} \right.}} \right.}} \right.} \\\left. \left. \left. \left. {\left. {2d_{1}^{N}} \right)\left\lbrack {4 - {\left( {1 - {2d_{3}^{N}}} \right)\left\lbrack {2 - \left( {1 - {2d_{5}^{N}}} \right)} \right\rbrack}} \right\rbrack} \right\rbrack \right\rbrack \right\rbrack \right\}\end{matrix}$ →Setting p = q = 1 or equivalently α_(F) = 21/1365 resultsin the traditional 4096-QAM constellation (64-QAM, 64-QAM) = 4096-QAMSuper-Constellation = For Scenario 1 (scalar/l-layer): For Scenario 2(two-layer): 1) 2p²(1344 + 21q²) = C, and 1)2p²(1344 + 21q²) = 0.5C(1 +α_(F)), and${{\left. 2 \right)\mspace{14mu} \frac{21q^{2}}{1344}} = \frac{1 - \alpha_{F}}{\alpha_{F}}},{{which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$${{\left. 2 \right)\mspace{14mu} \frac{21q^{2}}{1344}} = \frac{1 - \alpha_{F}}{\alpha_{F}}},{{which}\mspace{14mu} {arises}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {power}}$split requirement between (b₀, b₁, split requirement between (b₀, b₁,b₂, b₃, b₄, b₅) bits and (b₄, b₅, b₆, b₇, b₂, b₃, b₄, b₅) bits and (b₄,b₅, b₆, b₇, b₈, b₉) bits. b₈, b₉) bits

APPENDIX II Max-Log-MAP Soft Demapper Expressions

TABLE AII-1 Non-uniform (QPSK,QPSK) = 16-QAM Super-constellation$\quad\begin{matrix}{\mspace{191mu} {S_{p,\; q}\left( {X_{QPSK},X_{QPSK}} \right)}} \\{{L_{A}^{\prime}\left( b_{0} \right)} = {{{- \min}\left\{ {\frac{\left( {I - {a\left( {{2p} - q} \right)}} \right)^{2}}{4a},\frac{\left( {I - {a\left( {{2p} + q} \right)}} \right)^{2}}{4a}} \right\}} +}} \\{\min \left\{ {\frac{\left( {I + {a\left( {{2p} - q} \right)}} \right)^{2}}{4a},\frac{\left( {I + {a\left( {{2p} + q} \right)}} \right)^{2}}{4a}} \right\}}\end{matrix}$ $\quad\begin{matrix}{{L_{A}^{\prime}\left( b_{2} \right)} = {{{- \min}\left\{ {\frac{\left( {I - {a\left( {{2p} - q} \right)}} \right)^{2}}{4a},\frac{\left( {I + {a\left( {{2p} - q} \right)}} \right)^{2}}{4a}} \right\}} +}} \\{\min \left\{ {\frac{\left( {I - {a\left( {{2p} + q} \right)}} \right)^{2}}{4a},\frac{\left( {I + {a\left( {{2p} + q} \right)}} \right)^{2}}{4a}} \right\}}\end{matrix}$ L′_(A)(b₀) and L′_(A)(b₂) as a function of L′_(A)(b₁) andL′_(A)(b₃) as a function of I = Re (y_(cb)) for (QPSK, QPSK) (Q = Im(y_(cb))) for (QPSK, QPSK) I value L′_(A)(b₀) L′_(A)(b₂) Q valueL′_(A)(b₁) L′_(A)(b₃) I > 2Ip − 2apq − Q > 2Qp − 2apq − 2ap 2pqa qI 2ap2pqa qQ 0 < I ≤ I 2apq − 0 < Q ≤ Q 2apq − 2ap (2p − q) Iq 2ap (2p − q)Qq −2ap < I Iq + −2ap < Q Qq + I ≤ 0 (2p − q) 2apq Q ≤ 0 (2p − q) 2apq I≤ − 2Ip + qI + Q ≤ 2Qp + qQ + 2ap 2pqa 2apq −2ap 2pqa 2apq

APPENDIX II Max-Log-MAP Soft Demapper Expressions

TABLE AII-2 Non-uniform (16-QAM, QPSK) = 64-QAM Super-constellation$\quad\begin{matrix}{\mspace{365mu} {S_{p,\; q}\left( {X_{16{QAM}},X_{QPSK}} \right)}} \\{{L_{A}^{\prime}\left( b_{0} \right)} = {{{- \min}\left\{ {\frac{\left( {I - {\left( {{2p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{2p} + q} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{6p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{6p} + q} \right)a}} \right)^{2}}{4a}} \right\}} +}} \\{\min \left\{ {\frac{\left( {I + {\left( {{2p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{2p} + q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{6p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{6p} + q} \right)a}} \right)^{2}}{4a}} \right\}}\end{matrix}$ $\quad\begin{matrix}{{L_{A}^{\prime}\left( b_{2} \right)} = {{{- \min}\left\{ {\frac{\left( {I - {\left( {{2p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{2p} + q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{2p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{2p} + q} \right)a}} \right)^{2}}{4a}} \right\}} +}} \\{\min \left\{ {\frac{\left( {I - {\left( {{6p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{6p} + q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{6p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{6p} + q} \right)a}} \right)^{2}}{4a}} \right\}}\end{matrix}$ $\quad\begin{matrix}{{L_{A}^{\prime}\left( b_{4} \right)} = {{{- \min}\left\{ {\frac{\left( {I - {\left( {{2p} + q} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{6p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{2p} + q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{6p} - q} \right)a}} \right)^{2}}{4a}} \right\}} +}} \\{\min \left\{ {\frac{\left( {I - {\left( {{2p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{6p} + q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{2p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{6p} + q} \right)a}} \right)^{2}}{4a}} \right\}}\end{matrix}$ L′_(A)(b₀), L′_(A)(b₂) and L′_(A)(b₄) as a function of Ifor (16QAM, QPSK) I value L′_(A)(b₀) L′_(A)(b₂) L′_(A)(b₄) I > 6ap 4Ip −ap(8 + 4q) ap(8 + 2q) − 2Ip 6apq − Iq 4ap < I ≤ 6ap (4p − q)(I − 2ap)(2p − q)(4pa − I) 6apq − Iq 2ap < I ≤ 4ap 2p(I − qa) (2p − q)(4pa − I)Iq − 2pqa 0 < I≤ 2ap Ip 2ap(4p − q) − 2Ip Iq − 2pqa −2ap < I ≤ 0 Ip2ap(4p − q) + 2Ip −Iq − 2pqa −4ap < I ≤ −2ap 2p(I + qa) (2p − q)(4pa −I) −Iq − 2pqa −6ap < I ≤ −4ap (4p − q)(I + 2ap) (2p − q)(4pa + I) 6apq +Iq I ≤ −6ap 4Ip + ap(8 + 4q) ap(8 + 2q) + 2Ip 6apq + Iq

APPENDIX II Max-Log-MAP Soft Demapper Expressions

TABLE AII-3 Non-uniform (QPSK, 16-QAM) = 64-QAM Super-constellation$\quad\begin{matrix}{\mspace{464mu} {S_{p,\; q}\left( {X_{QPSK},X_{16{QAM}}} \right)}} \\{{L_{A}^{\prime}\left( b_{0} \right)} = {{{- \min}\left\{ {\frac{\left( {I - {\left( {{4p} - {3q}} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{4p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{4p} + q} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{4p} + {3q}} \right)a}} \right)^{2}}{4a}} \right\}} +}} \\{\min \left\{ {\frac{\left( {I + {\left( {{4p} - {3q}} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{4p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{4p} + q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{4p} + {3q}} \right)a}} \right)^{2}}{4a}} \right\}}\end{matrix}$ $\quad\begin{matrix}{{L_{A}^{\prime}\left( b_{2} \right)} = {{{- \min}\left\{ {\frac{\left( {I - {\left( {{4p} - {3q}} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{4p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{4p} - {3q}} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{4p} - q} \right)a}} \right)^{2}}{4a}} \right\}} +}} \\{\min \left\{ {\frac{\left( {I - {\left( {{4p} + q} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{4p} + {3q}} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{4p} + q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{4p} + {3q}} \right)a}} \right)^{2}}{4a}} \right\}}\end{matrix}$ $\quad\begin{matrix}{{L_{A}^{\prime}\left( b_{4} \right)} = {{{- \min}\left\{ {\frac{\left( {I - {\left( {{4p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{4p} + q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{4p} - q} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{4p} + q} \right)a}} \right)^{2}}{4a}} \right\}} +}} \\{\min \left\{ {\frac{\left( {I - {\left( {{4p} - {3q}} \right)a}} \right)^{2}}{4a},\frac{\left( {I - {\left( {{4p} + {3q}} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{4p} - {3q}} \right)a}} \right)^{2}}{4a},\frac{\left( {I + {\left( {{4p} + {3q}} \right)a}} \right)^{2}}{4a}} \right\}}\end{matrix}$ L′_(A)(b₀), L′_(A)(b₂) and L′_(A)(b₄) as a function of Ifor (QPSK, 16QAM) I value L′_(A)(b₀) L′_(A)(b₂) L′_(A)(b₄) I > (4p +2q)a 4Ip − 12pqa 2aq(q + 4p) − 2Iq 2aq(2p + q) − Iq 4ap < I ≤ (4p + 2q)a(4p − q)(I − 2aq) 4apq − Iq 2aq(2p + q) − Iq (4p − 2q)a < I ≤ 4ap (2p −q)(2I − 2aq) 4apq − Iq Iq − 2aq(2p − q) 0 < I ≤ (4p − 2q)a I(4p − 3q)2qa(4p − q) − 2Iq Iq − 2aq(2p − q) −(4p − 2q)a < I ≤ 0 I(4p − 3q) 2qa(4p− q) + 2Iq −Iq − 2aq(2p − q) −4ap < I ≤ −(4p − 2q)a (2p − q)(2I + 2aq)4apq + Iq −Iq − 2aq(2p − q) −(4p + 2q)a < I ≤ 4ap (4p − q)(I + 2aq)4apq + Iq 2aq(2p + q) + Iq I ≤ −(4p + 2q)a 4Ip + 12pqa 2aq(q + 4p) + 2Iq2aq(2p + q) + Iq

What is claimed is:
 1. A method of selecting a superpositionconstellation comprising two or more user equipment (UE) constellations,comprising: determining which type of superposition constellation(super-constellation) to generate based at least on a power ratio amongthe two or more UEs, wherein one type of super-constellation is aGray-mapped Non-uniform-capable Constellation (GNC), in which both theconstituent constellations of the two or more UEs and the GNCsuper-constellation itself are Gray-mapped; and when the determined typeof superposition constellation is the GNC super-constellation,generating the determined type of superposition constellation by mappingthe GNC super-constellation from outermost bits to innermost bitsaccording to each of K number of UEs.
 2. The method of claim 1, wherein,if each of the K UEs uses Quaternary Phase Key Shifting (QPSK)modulation for a single-user constellation, mapping the GNCsuper-constellation can be represented by:(b ₀ ,b ₁ ,b ₂ ,b ₃ , . . . ,b _(2k-2) ,b _(2K-2))=(b ₀ ,b ₁)⊕(b ₂ ,b ₃). . . ⊕(b _(2K-2) ,b _(2K-1)), where (b₀, b₁) are two bits for a firstUE and the outermost bits, (b₂, b₃) are two bits for a second UE, and soon, until (b_(2K-2), b_(2K-1)), two bits for a Kth UE and the innermostbits.
 3. The method of claim 1, wherein determining which type ofsuper-constellation to generate comprises: determining whether toperform bit-swapping among the two or more UEs in thesuper-constellation.
 4. The method of claim 1, wherein determining whichtype of super-constellation to generate is also based on at least one oftarget throughput, target Block Error Rate (BLER), Modulation and CodingScheme (MCS) of at least one of the two or more UEs, and the MultipleInput Multiple Output (MIMO) rank of at least one of the two or moreUEs.
 5. The method of claim 1, wherein determining which type ofsuper-constellation to generate comprises: finding the type ofsuper-constellation in a look-up table (LUT).
 6. The method of claim 1,wherein the two or more UEs comprise K number of UEs and determiningwhich type of super-constellation to generate is based at least onvalues of α₀, α₁, α₂, . . . , α_(K-1), where α_(i) is the transmissionpower allocated to UE_(i), and α₁+α₂+ . . . +α_(K-1)=1.
 7. The method ofclaim 6, wherein which type of super-constellation to generate isdetermined based at least on whether one or more values of α₀, α₁, α₂, .. . , α_(K-1) being greater than, equal to, or less than a threshold. 8.The method of claim 6, wherein which type of super-constellation togenerate is determined based at least on whether one or more values ofα₀, α₁, α₂, . . . , α_(K-1) fall within one or more range of values. 9.An apparatus for selecting a superposition constellation comprising twoor more user equipment (UE) constellations, comprising: at least onenon-transitory computer-readable medium storing instructions capable ofexecution by a processor; and at least one processor capable ofexecuting instructions stored on the at least one non-transitorycomputer-readable medium, where the execution of the instructionsresults in the apparatus performing a method comprising: determiningwhich type of superposition constellation (super-constellation) togenerate based at least on a power ratio among the two or more UEs,wherein one type of super-constellation is a Gray-mappedNon-uniform-capable Constellation (GNC), in which both the constituentconstellations of the two or more UEs and the GNC super-constellationitself are Gray-mapped; and when the determined type of superpositionconstellation is the GNC super-constellation, generating the determinedtype of superposition constellation by mapping the GNCsuper-constellation from outermost bits to innermost bits according toeach of K number of UEs.
 10. The apparatus of claim 9, wherein, if eachof the K UEs uses Quaternary Phase Key Shifting (QPSK) modulation for asingle-user constellation, mapping the GNC super-constellation can berepresented by:(b ₀ ,b ₁ ,b ₂ ,b ₃ , . . . ,b _(2k-2) ,b _(2K-2))=(b ₀ ,b ₁)⊕(b ₂ ,b ₃). . . ⊕(b _(2K-2) ,b _(2K-1)), where (b₀, b₁) are two bits for a firstUE and the outermost bits, (b₂, b₃) are two bits for a second UE, and soon, until (b_(2K-2), b_(2K-1)), two bits for a Kth UE and the innermostbits.
 11. The apparatus of claim 9, wherein determining which type ofsuper-constellation to generate comprises: determining whether toperform bit-swapping among the two or more UEs in thesuper-constellation.
 12. The apparatus of claim 9, wherein determiningwhich type of super-constellation to generate is also based on at leastone of target throughput, target Block Error Rate (BLER), Modulation andCoding Scheme (MCS) of at least one of the two or more UEs, and theMultiple Input Multiple Output (MIMO) rank of at least one of the two ormore UEs.
 13. The apparatus of claim 9, wherein determining which typeof super-constellation to generate comprises: finding the type ofsuper-constellation in a look-up table (LUT).
 14. The apparatus of claim9, wherein the two or more UEs comprise K number of UEs and determiningwhich type of super-constellation to generate is based at least onvalues of α₀, α₁, α₂, . . . , α_(K-1), where α_(i) is the transmissionpower allocated to UE_(i), and α₁+α₂+ . . . ++_(K-1)=1.
 15. Theapparatus of claim 14, wherein which type of super-constellation togenerate is determined based at least on whether one or more values ofα₀, α₁, α₂, . . . , α_(K-1) being greater than, equal to, or less than athreshold.
 16. The apparatus of claim 14, wherein which type ofsuper-constellation to generate is determined based at least on whetherone or more values of α₀, α₁, α₂, . . . , α_(K-1) fall within one ormore range of values.